> never displays or updates apps correctly. Half the time an app showed up on the website that didn't show up on the phone app. The other half of the time even when I did get something installed, it would just never understand that an update existed and needed to download and update a given app
You probably "just" need to pull down while on the "Latest" or "Updates" tab, to update your repository (it will show a small banner at the top while it's doing that). It's incremental, so it may take a while if it has been some time since you last did it (and auto-updates are disabled).
The way F-Droid works is that it downloads the whole index and then the catalog, version checks, etc, all runs locally, quite similarly to some package repositories actually.
I am not claiming its intuitive, but I think that part works fine once you understand how it works.
The last time it wouldn't update an app, I could see in the app store and on the website that my app had a new version, but no matter what I did, I could not make it update the app. I don't know what I was doing "wrong", but I think if I couldn't figure it out or make it happen, there's something very wrong with either the app or how it's "supposed" to work. Neither of which is an acceptable user experience for me.
Ok, you clearly don't know what F-Droid is.
F-Droid builds all apps by themselves, which especially with their old servers took a lot (between detecting that the update exists, building the app and going to sign everything at their air-gapped signing computer).
Now a lot of apps use the "reproducible builds" feature, which means that F-Droid will distribuite them as they come from the author, leaving their digital signature; but they still need to build those apps before distributing them, to verify that what the author built corresponds to the declared source code.
With the much powerful servers that they've had for a few months builds are a lot quicker, but there are still steps that can take several days, especially the part of signing the apps' index on their air-gapped computer.
There's a ton of things that could be improved, and it would be best if there were an alternative with better maintainers, but they're currently the only service of this kind for Android (well, IzzyOnDroid is a partial alternative, if you're careful to check their reproducible builds results).