What is your personal definition of "Productivity" and what do you think is its end goal?

Accomplishing things. Getting work done. Whether it's work done for survival, something more abstract like your desk job, or personal goals like chores around the house.

Productivity is when your boss makes you overwork yourself and pockets the difference 👍

It's when doing actions/work gets you closer to a goal

Productivity is a measure of output completed whithin a time frame. This could be goods, services, or even personal goals as long as the output is measurable in some way and it was completed within a realistic time frame.
Washing dishes, losing weight, and making children happy can all be counted as productive if there are goals and a way to measure them. Even reduced anxiety by taking s day off could be described as productive if there is a way to measure it even if the measure is subjective. Cleaning up a park can be productive even though the end result is removing things instead of creating them!
Basically it is getting things done within a reasonable time frame and is not limited to business.

What you can accomplish given a fixed set of resources. Not to be confused with efficiency, which is how much those resources can accomplish in a given amount of time.
- I would call that resourcefulness, and make productivity a function of resourcefulness × efficiency.

It is a measure of how your actions get you closer to your goals.
Hence, if my goal is learning Japanese, and I spend time in reading raw manga, I can argue I'm being productive. However, if my goal is to learn Rust, then reading raw manga is not being productive.
Productivity does not have an end goal other than what you set for yourself.
EDIT:
Edited the last sentence to make it say what I meant it to say. "Productivity has an end goal…" isn't it. 😅

Productivity is simply a measure of what is produced.
American culture usually measures this as what gets done (work, chores and errands, creation of things, etc). I think that this is sort sighted. It can be productive to rest and instead produce energy in order to do other things later.

For my life? Productivity I would measure as what gets done in a certain time period. Some days I get a lot done, work and exercise and cook and garden - high productivity days. Other days I do less and rest, unproductive days. That's balanced.
For an economy? Production/number of employees. That's the # that keeps increasing here while real earnings/employee decreases.

Being a able to get into the flow state to solve the task in question

It's a pretty broad term. In a personal sense? In an economic sense? Need some context.
- Surely that's the point of OP's question.
  
  I doubt it. If you don't provide context, people will provide their own context. And then the question is just a kind of Rorschach test.
- Personal.
  
  In a personal sense, I define productivity mainly as objectively measurable accomplishment over a period of time. If I used time productively, I either improved my circumstances (or my employer's circumstances, when they're paying me for my time) or worked towards that improvement in a permanent way. Research and learning is productive, when it furthers my ability to improve my circumstances. Research and learning for its own sake is only mildly productive in that it makes me a more knowledgeable person.
  Leisure activity is NOT productive, mostly, but that's not a bad thing. The main thing is to avoid COUNTER productive activities. Leisure activity is somewhat productive when it allows me to rest and recuperate and be more productive later.
  Productivity involves "getting things done" but only when those things matter. Making my bed every day has no discernible benefit to me, so that time is not spent productively. The dude in front of my house with his loud-ass leaf blower spending an hour blowing a single leaf all around the street is not being productive. Sure, it's more productive than sitting catatonically, but not by much. It's productive to him in the sense that he's getting paid for that time, but it's not productive on behalf of his employer (who is, in a sense, me via my landlord).

Productivity is feeling satisfied with what you have achieved. Goal is a sense of purpose.

Productivity is part of the dominant theology of (at least) Western culture and functionally extends and replaces the societal functions of christian (also other religions) conservatism to centralize power in a rigid and defensive structure of guilt and judgement.