> 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.