Oh, it fails to install anything when Obtainium does not find an installable build.

That's because not every git repo necessarily hosts installable builds at all. The main purpose of git is just to host the source code for that project. With that said, many repos do also build an installable release (*.apk, *.exe, whatever) of each major version and host that in the "Releases" section.

As an example, here is Obtainium's GitHub repo. If you scroll to the bottom of the page, you see the "Releases" section that contains the most recent APKs and everything:

But not every git repo hosts releases. Eddie is one of those. The git repo for Eddie is just for hosting the source code. They host the releases on their own website instead. In that case, you can often just take the URL for whatever website is actually hosting the APKs and paste that into Obtainium and it will do its usual web scraping method to find the appropriate APK files for each update.

On the other hand, that web scraping often does not work and requires more complicated techniques to get Obtainium to find the appropriate APK files. That is where https://apps.obtainium.imranr.dev/ comes in handy. This is a crowdsourced list of popular apps that require more complicated techniques to add to Obtainium, and each has a neat little "Install" button to quickly and easily add that app to Obtainium by applying that complex config in the background for you.

But there are also some projects that don't host releases anywhere other than F-Droid. In that case, by all means, just use F-Droid for that app.