You have to add them manually, either by url or with the built in search. For example, you can add newpipe by searching sources and checking github as a source to search. It will then show you repos that match newpipe, which usually is the regular newpipe repo and then a bunch of forks of it.
Obtainium isn’t for finding FOSS apps, it’s for installing them. To find them, you can check out existing repos such as f-droid or izzy, or you can ask around. This post has a bunch of recommendations in the replies
Obtainium lets you install FOSS programs directly from the developers source. You can get updates from the github/gitlab of app developers before they get uploaded to F-droid.
Lossless CutFOSS, Crossplatform frontend for ffmpeg. Note that to do it losslessly, it will still be in mp3. If you need to transcode you can do that too, but like others have said you’ll probably lose quality.
If you really don’t want to spend money, there’s always GNU Octave. Sure, it doesn’t have the thousands of matlab toolboxes, but if you’re running code from 40 years ago it shouldn’t need those anyway. I wrote a couple of scripts recently and then rewrote them slightly so that they would be compatible with octave.