I don't encounter all the same bugs gp does, but I do encounter several on a regular basis. These issues show up regularly on both my tablet and my phone, and they showed up regularly on my previous phone and two tablets over a range of ~5 versions of Android (8-12)
1. Every so often I turn on my tablet or phone and see a notification that fdroid has crashed, asking me to submit the information (I used to, I don't anymore). I wasn't using fdroid recently, I don't leave it open in the background; the only background task it has is fetching update lists and downloading new versions to install later. If it crashes, it loses the downloaded updates.
2. Occasionally fdroid crashes on start, providing the same notification as above. Force-stopping the app and removing the activity from recents is the only way to get past this--if I force stop and restart from recents, it crashes again. If I remove from recents and don't force stop, it crashes again. I'm guessing whatever parameters it launched with are causing the crash to happen again.
3. The background service frequently stops while updating package lists (not while downloading packages). The notification remains. This is regardless of whether the update is manual or automatic; there is no foreground update. At 11:00pm I regularly have a non-dismissable sticky notification, last updated at 5:00am, that fdroid is updating repos. Tapping it does nothing, I have to open the fdroid app, which may or may not crash on opening. If it crashes, the only way to reset the notification is to force-stop it. This is also the only way to open fdroid after such a crash (see #2). While I have no confidence that the crashing issue is fixed, it sounds like the new index is intended to prevent repo updates from taking this long. Personally, I'd prefer to just download an SQLite file directly from a server and just dump that in the app to query.
4. After downloads are complete, the download list frequently doesn't update. I can initiate the install from either the page for that specific app or from the download notification, but the main downloads list just shows that it's still downloading.
5. Not really a bug so much as missing feature: there's no way to do partial update checks. No way to check for updates to a single app without downloading the entire repo. I know there's an update available for X Y Z apps and want to update them on the bus, but because #3, 30 minutes is likely not long enough to do so. There's also no way to check a single repository for updates, and trying to bypass this by toggling that repo off and back on causes fdroid to update all repos in the order they were added. If I want to install an app from a new repo, I have to wait for all my other repos to finish updating first.
6. I have ~10 repos in fdroid. I regularly get a notification that the format is incorrect or the server couldn't be contacted or some such. It doesn't tell me what repo that is. My only option is to go through and toggle all my repos off, enable them one at a time, and
I've mostly given up. I can't get the latest update for apps from the website because fdroid doesn't make that available, I can't install updates automatically because I'm not rooted (and thus can't just trust that it'll eventually succeed in installing). I used to run my own fdroid repo for these apps; I don't anymore, because it's not worth the effort to try and get fdroid to install them.
It's not because I'm using some obscure hardware or ROM; I've had these issues with: Nexus 7 lineage, Nvidia shield lineage, Moto G6, Moto G6 lineage, Samsung A32 stock, Samsung Galaxy Tab S6 stock. Fdroid is usually the first thing I install after getting a new device or after rooting a device; I've had fdroid crash on the third time starting it on a brand new device, before I've done more than enable adb to install fdroid.
*This is _not_ a one-off case, this is an ongoing issue that I've had for years at this point*
Instead, for the few apps I actually care about keeping up to date, I use Obtainium, which checks GitHub releases (among others) instead of fdroid (it can check fdroid's website, but that's not kept up to date). As a bonus, this also allows me to keep track of apps that aren't included in fdroid (mostly Tachiyomi forks). Obtainium can't check for updates for individual apps without fetching and parsing the entire catalog, because fdroid only provides a full catalog (see #5)