This may or may not be the answer you are looking for, but I have taken a very big interest in Personal Information Management (PIM) over the years and tried out many different systems and thought about the subject quite a lot.
I became so frustrated over the years running into so many dead ends (lacking functionality), incompatibilities (often times purposefully (i.e., proprietary software, walled garden, vendor lock-in, etc...), arbitrary limitations, etc. that I have moved more and more not only into Free Software but also making sure I stick to open protocols and formats. Because I just don't have the time nor energy any more to keep re-inventing the wheel all the time, learning new software, moving my work/information between incompatible systems, etc...
In particular I have gravitated towards using text files as a sort of lowest common denominator universal format. This began for me when I was trying to synchronize bookmarks across several different browsers and OSes (which, at the time, happened to be Android and Windows). I ended up just learning basic HTML and making my bookmarks in a handful of interlinked files. Totally universal, fully customizeable, and available on any platform with a browser (where you would need to use the links anyway).
I could go on and on but I will try to get back on the topic of Project Management. Around the same time I started thinking that text files were the answer to data portability, I was also becoming aware of (what I now think is) the best tool I have ever found for editing text, Emacs. And then when I discovered Orgmode, it was all over. Now, remember that the underlying file remains simple plain text, but Orgmode gives you:
outlining (nested levels, etc.)
tagging
hyperlinks (to urls as well as local files, certain locations in other files, emails(!), etc.)
small tables / spreadsheets (including math!) right in the middle of your notes [1]
TODO functionality
time / date stamps, timers, etc.
functional (!) code blocks [2]
full text search
and many more
Note 1: This is an incredibly useful and often used feature for me. See around 6:03 in the first, or 6:57 in the second video, below.
Note 2: What this means is you can put some code of a certain type in a code block, open the code block in a mini editing mode for that particular language (including syntax highlighting, completion, etc.) and even execute the code. Pretty far out. Also very useful for code snippets of Arduino (which is just C++ really), or anything else, really... See 12:40 in first video.
Well, I didn't really "get it" until I had watched a couple videos:
This video is longer, but was one of the ones that convinced me (actually I think I only got like halfway in before my mind was so blown that I had seen enough and was convinced ) :
Getting Started With Org Mode – 56:21— thoughtbot
Here is a shorter one that you may prefer instead:
org mode is awesome – 18:07— John Kitchin
Although I recommend eventually watching them both (if/when you have time).
You can then go on to synchronize your files using something like Syncthing across all your devices, or if you prefer, self hosted Git as you mentioned (I use either/both, depending on nature of the information) as they are just text files at the end of the day (perhaps with some linked related design files, etc.).
I think it may be the only software I have ever used where I have yet to run into any sort of limitation. Not only that, but by now (a couple years in) I have even started writing some (rudimentary) Lisp functions to do custom things the way I like. For instance I made myself a "photo tagging mode" that operated exactly the way I wanted.
I think this is because (almost) the whole thing (Emacs) is written in Lisp, and therefore is extensible. And as you can imagine, when you put this sort of tool into the hands of hackers and give them 40+ years(!) to hack on it, well you can imagine what they can and have come up with. It is sort of a running joke that Emacs is more of an "operating system" or "environment" than a "text editor" but it is also very true.
I have not looked for specific additional tools for Project Management as you ask for, per se, within Emacs because I have not felt the need for them, personally. However, if you look around, it would not surprise me at all if you found something that may tickle your fancy...
Now there is a famous learning curve, and I will not deny this. I took me several times coming across information about Orgmode before I became interested enough to take the plunge. And then it took me a couple/few attempts to get off the ground with Emacs (you might find the basic navigation "weird" at first by modern standards, but now that I am used to it, I actually have my entire OS set up to work this way [3]). Anyway this is a fair criticism.[4] But now that I am over that initial hump, I feel like there is pretty much no situation that I cannot accommodate within this system I have learned. So I view it a a worthwhile tradeoff of my time for a very, very powerful tool that can do, well, pretty much whatever I can imagine. And Orgmode is just the "killer app" or "gateway drug" into Emacs... There is a ridiculous amount of other things you can do with it...
Note 3: Yes! This is possible in XFCE(!)
Note 4: If anyone is interested, I can give some pointers. Basically, sit down when you are not in a rush to produce some results "right now" and therefore in a proper mindset to learn. Like a weekend morning, or something like that. Get yourself a nice cup of coffee or your favorite beverage and start working through the built in tutorial inside Emacs. It really is great and gets you going starting from zero by baby steps.
