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.
We search for stuff, install it, it updates in the background. We install some of our own repos, but the bulk of our apps come from F-Droid's default repos.
Hard to reconcile your account with my experience without specifics.
I very much prefer Obtainium these days despite the setup steps. I don't think it's a coincidence that Obtainium, Aurora, Zapstore, etc. are gaining mindshare over F-Droid, just like how Brave has explosive growth over FF.
https://github.com/rumboalla/apkupdater
though personally I use it only for Fdroid, Gitlab and Github
Sounds like an accurate recreation of the Play Store experience to me.
You're sure you understand what it does?