When is it the right time to give up?

There's no one answer fits all.
On life? Never. On your goals? Depends. On self-destructive behaviour? Now. On those you love? Never. On business ventures that don't take off? You tell me.
Point is: life is rarely black & white. Treat it with the color and nuance that makes it what it is.
- Why never on life, just asking. If it was completely ruined from the start, why not give up? If you spill ink over a painting, it's ruined and you toss it out.
  
  Sure, life can be incredibly tough, and it's understandable to feel overwhelmed at times. However, unlike a painting, life isn't a static object. It has ups and downs, and even when things seem completely ruined, there's always potential for change, growth and even thriving. I actually have a little experience with that.
  Staying with your analogy: if you spill ink on a painting, you might see it as ruined at first. But some artists use those accidents to create something new and beautiful. Like so, life can take unexpected turns, and what seems like a disaster now might lead to new opportunities. I am the person I am partly due to troubles and disasters in my life. Could I do without those? Sure. Should I? Not sure.
  That all said, if you're feeling like ending it all I can only encourage you to reach out for support. Talking to friends, family, or a mental health professional in your area can make a big difference.
  Your life is valuable. You are important and valuable.
  You're not alone. Definitely not with life. There are people who care about you and want to help.
  
  The japanese philosophy of Kintsugi may help you look at things differently. Impurities are what make us all unique. Nothing in nature is perfect.
  https://www.bbc.com/travel/article/20210107-kintsugi-japans-ancient-art-of-embracing-imperfection
  
  It's practically impossible to fix a painting covered in ink. It's never too late for a life to change.

I’ve seen you struggling with existential questions a lot here. Are you going to therapy?
- There are so many people who deserve it more, now why would I block them from receiving help, so I could be an even bigger burdensome waste of resources? Bruh, come on. My mother literally took food from a food bank that she didn't need, made each family member (except me because I'd escape) do it and take 4 times the amount alotted to each household, to just NOT use. Literally wasting resources that someone in need could use. Why would I do that myself?
  I'm just saying if your life was ruined at the start then it's ruined forever, either continue living a ruined life or give up.
  
  Hatte to be mister smarty-pants here, but empirically if your life was ruined from the start, your chances of recovery through therapy are actually much higher then for someone who ruined it himself/got Ill later on in life.
  The thing is: finding therapy that works for you is a process on its own. You will likely have to try a lot of them to find a good one who has free slots. But you will find one eventually and if you have it does help!
  Just one word of caution: go to to ones who actually have a Dr./major/magister in psychology and are registered doctors.
  I hope you life in a country with good universal healthcare, if so you can just go to a therapist (they offer single sittings for cases like that) and discuss with him what kind of therapy could work for you and what the next address can be.
  I am someone who is not religious and believes everyone should have a free decision if they want to live or not, but my galeart says: man, don't give yourself up, especially not because of damage inflicted on you by others. All the best from germany
  
  You have all the right to claim a spot in society and use the resources it offers you. It is not wasted! You can turn things around if you really try. I would really urge you to seek out therapy.
  
  I'll say I've definitely struggled with the same feelings of someone else being in greater need than I am. And from my perspective, you are the person that deserves it more.
  Have you ever thought about the first painful sensation a baby ever has? They have no frame of reference for it, and so in that moment it will have been the worst pain they have ever experienced. But to an older person, that same pain is probably just a pinch on the wrist. Does that mean that nobody should console the baby? Ease its pain? Maybe there are people in greater pain than you, or maybe you are the one in greater pain, and unless you have the ability to live another person's experiences one-to-one, you will never know for sure. All that matters is that you are hurting. Don't deprive yourself of help just because of some torturous hypothetical.
  
  You are someone in need. You're not sponging resources. These resources are there to be used by someone who needs the help. You do.
  You're also not your mother.
  You are around 20 years old? Means you likely have many more ahead of you. I had a couple of massive twists and turns in my life. Some within, some outside my control. I know enough people who will say the same. You simply don't know what will happen tomorrow. Anyone who claims to even know what exactly the weather will be like in two weeks is just not telling the truth, let alone what a human life will be like tomorrow or in a few years.
  Keep going! You only have one life. You don't know what's coming.

when its not giving up but moving on.

Regularly assess the goals that you had when starting the endeavor and decide if you'd start the initiative then if you had the information you have now. What investment is lost if you stop now?
If this is about relationships, that's another story.

After you spoke to a therapist

"If at first you don't succeed, try, try again. Then give up; don't make yourself look like a fool."
Can't remember where I first saw that quote, but it stuck with me.

Hmm, let's ask Rick Astley that one.

I like your questions blues. I feel we have come from similar backgrounds. I've just passed the 20s, and my life has been not worth it. I'd be relieved to die any day (or to have died at any point prior). My parents were abusive, my extended family were dysfunctional, and my childhood was isolation incarnate. I think this question's heading is life, although it skirts around that. Suicide is painful. If anyone manages to commit then that's the right time for them. It really is not something one can just "choose". It's not a choice.
I don't think material conditions play much into this decision, though when articulated it may appear they do. "I don't have friends," "I don't have a car", "I don't have a non-degrading job", "I don't have a house", etc. It's a feeling. One could have everything they thought they craved and still feel miserable and despondent. One could have nothing and be in high spirits. I don't think anyone knows how to control emotions enough that they're able to guide someone to a social 'norm'. I'd suggest engaging with doctors though, and that ranges through to the general practitioner to the specialized psychiatrist, and all those professions in between.
History abounds with morose writings. It's not a new question, and I don't think it'll ever have a definitive answer. Just keep trying different things, and keep talking to others as much as you can, because whilst an individual might not have a definitive answer you usually can find something with enough data.

not yet...
not even two days from now.
- Honestly if I don't have $100,000 by 11/25 I'm ending it.
  
  how are you going to get $100,000?
  
  Im also killing myself on the 25th lol. During my partner's exam I'm going to my favorite bench, drinking a bunch of benzos and vodka, and then shooting myself. Ive had it planned for a while. Life isn't worth living anymore. I have too many mental health issues and trauma and have been fighting too long and can't imagine fighting for another 50 or 60 years.
  I have thought about killing myself every day of my life since middle school and it is so freeing to have a solid plan and todo list of what I actually need to finish before I get to kill myself. I've tried before but I realize now I didn't actually want it as much then. I finally feel calm. I'm finally ok with just being a statistic.

You don't give up ever.
You pursue a better solution whenever one presents itself.

When a better path forward has presented itself

There are things I've put a long, long "pause" on, just to avoid frustration. But I approach most things like an animal pacing a cage, always looking for a way through.
Never discount the power of small success, consistently repeated. If you're making progress, no matter how small, you're making progress.

On life? If I have an extremely disabling condition to my mind or I can expect to die soon with a very low quality of life.
I don't see addiction as being that disabling as there are a lot of available resources to treat addiction and a high enough success rate to try.

I have felt before like "nothing's going right and nothing is ever going to go right" as you seem to be.
Only the first half of that feeling might be true and the second is definitely untrue. It's not going to be perfect either, but it will be a mix of nice things, amazing things, annoying things and awful things.
If something is not working, try something else. That "something else" may be another method to get it work, or it may just be replacing your original goal with a different one.
Either way, success will come to you, as long as you take care of yourself and keep in good health, are open to broaden your definition of success and not focus on a singular objective that everything must go perfectly as planned. You've made it this far in life, that is a success in itself and I know you are capable of much more when you set your mind to it.
There are lot of things you can give up, the main thing is not to give up on yourself. Take breaks as you need. Start by fixing even the tiniest thing that needs fixing in your life, like picking up one sock off the floor, or wiping down your bathroom sink. Instead of thinking you've lost everything, start from what you have and build from there.
Even in the best of times, there's been news that has brought despair to me. The way to overcome it is to tune it out a bit, with music, with fresh air, or if it's a chronic problem, with therapy and treatment based on a physician's recommendation, and reframe your focus to things you can accomplish, have accomplished and will accomplish.

https://en.m.wikipedia.org/wiki/Diminishing_returns

never.

I think putting over 10 years towards a goal and never achieving it means you should just give up
- Cutting ties with family and moving out. Every apartment costs at least 20% more than I make monthly, a mortgage is out of the question after losing my credit last year, and working while living with these people is not sustainable. Every roommate is basically family but worse and there's no way I'm moving out from living with family to live with someone worse than family. Even if I find roommates that aren't nicotine or marijuana users, they'll be something worse the minute I'm stuck with them. No one knows how it feels being the only person who doesn't use that stuff, and being antagonized by groups of people withdrawing from it.