Free project organisation software?

I don't have a specific software recommendation but this sounds like something you could represent with a Gantt chart. There are some applications that focus specifically on these charts or they may just be one document type out of many to choose from. Using the terms "Gantt" and "FOSS" in a search engine should bring up some useful results.

food for thought, feel free to totally toss away and ignore

Personally I don't recommend finding some random simple notes app because you will likely use it for awhile, run up into a limitation and eventually abandon it.

I recommend you invest your time in a software or system that can grow and shrink with the amount of spoons/degree of hyperfocus you have to spare on the system. It should be brutally simple to open a note and start writing and not make you feel like haphazardly tossing a couple of bullet points onto a page is using the tool wrong (like a barely used planner with weeks and weeks of empty days staring you down with shame).

On the other hand ideally it should be capable of expanding along any direction your mind wants to go without shackling you to a system that won't satisfy whatever ridiculous and capricious bullshit system you come up with whenever your hyperfocus-eye-of-sauron turns for a brief but glorious hot second onto the topic of organizing yourself. Your tool needs to be able to instantaneously fold up from a gargantuan all encompassing idea processing machine to a glorified digital post it note in the snap of a finger, otherwise if you are like me than you will just abandon the byzantine complexity of it whenever you go through an "organizational winter" (and you will never stick with a more limited tool in the first place).

I also recommend you to try to find a tool that is open source, organizational tools are too long lived and vital to be entrusted in the whims of whatever company gobbles up the company that originally made your organizational app of choice.... that maybe you accidentally balanced your ability to live a functional life on somehow when you weren't paying attention....

I recommend:

Joplin https://joplinapp.org/

Logseq https://logseq.com/

I recommend these tools because you can trust that you can develop a long term relationship with them (HABITS), that you can have control over the details of so you can tweak something to fit your needs if you really need to (if you are like me and hate organizing yourself, the smallest detail in an app can ruin it like a menu bar that I can't get out of the way and hide when I am focusing) and that your system and associated habits will never be lost, locked up in a proprietary data format/app that becomes abandoned when the company goes out of business. Learn to use Joplin or Logseq as a dumb simple notetaking app, keep your use of it extremely straightforward and simple and then as the years go by if you feel like it, learn little by little how broader uses of the tools are possible and let them slot naturally into your life.

That is just my advice though!

(edit I use emacs org-mode which is like these but I wouldn't call it simple necessarily, but I wouldn't hesitate to use joplin or logseq as an alternative they are both mature tools with deep functionality that also let you use them like a simple dumb notepad to jot ideas down in)

Personally I like Jira a lot (and it's free for up to 10 users), especially as it is easy to integrate with Confluence for knowledge retaining. Asana is nice for absolute project newbies, but is less ideal for multiple projects and more complex requirements. MS projects is utter garbage.

If you want something self hosted and free it's much more difficult. I tried basically all of them - Open Project, Leantime, Taiga, Redmine and a few more. For my private projects I prefer Redmine, it looks old as fuck, but can be customised heavily and is none of these "pseudofree" systems that do only make the basic version free but make you pay for otherwise essential features (custom fields!).

YouTrack is useful.

Found Miro today, seems handy.

I've never used it but Leantime promotes itself as tailored for ADHD and neurodivergence in general. I believe it has a free option, or you can self host also for free.

Steptup time is frustrating but I like lunatask and Trello. Both have free options that might meet your needs.

Joplin looks pretty damn good, my question is about the diagram function - basically, I take on more than I can manage, and have made my life a bit of a tangled hellscape. I’m looking to visually organise the physical projects I have started, and see which parts are holding up other projects. Essentially, columns of blocks for steps to complete one thing, each block being its own note, and visually showing if there are steps in other columns on which this block depends, or depends on this. Can it do that?

The way you describe these programs, and their websites suggest that they’re actually going to be way more useful than just my intended use case, I’ve never really considered replacing my basic notes with something like this. I used Evernote for a while, but they made more and more features paid, and it got much less useful in comparison to the iOS notes app, so I’ve just stuck with that for ages. What you say about a mature app with continued support really matters. Photobucket are working their absolute hardest to prove that point at the moment.

ClickUp has been working for my work projects. There's a free and a paid version. Free should work for most people.

There's a "blocking" feature so you can see what parts of the project need to be done first, the ability to create templates (and schedule tasks based on the start or end date), recurring tasks, etc. I think there's a bit of a learning curve and sometimes I have to go digging or contact support because i can't figure out how to do a particular workflow, and sometimes the answer is "it's in the works" and sometimes it's the case of a hidden setting.

I use AnyType but I'm not sure that's what you're looking for. It's very similar to Notion

@TheBiscuitLout I often use the free version of AceProject.com

Todoist

Im really fond of Azure DevOps backlogs at work, and wish there was an exact 1:1 open source version that could work offline or in combination with something like nextcloud. The structure is incredibly flexible and can easily be used for life stuff (its not just for software development or professional work!)