F-Droid Basic is cool. Same thing, just without some sharing options etc., you probably don't use anyway. It was the first one to get actual background updates on modern android.
Barcode Scanner is decent, it even searches for products online, if you scan something that looks like a food label etc.
Casio G-Shock Smart Sync if you are tired of official Casio app in a casio bluetooth watch.
DuckDuckGo is there...
FadCam - if you ever need a recording without tracking attention (while phone is locked). Could get you out of some legal trouble...
Futo Keyboard is interesting project.
GadgetBridge saves some old devices. I use it for some Xiaomi eink devices that overwise require... to be connected to chinese datacenter to be discovered and sync. Which is insane, as some versions discover and can be synced on EU servers...
Grayjay for videos on many platforms.
So many HackerNews clients - I'm on Hacki currently.
Home assistant, Jellyfin, Joplin, Mullvad, Telegram, Nextcloud, Organic Maps, Osmand~, Tailscale or Yubico authenticator are all there. I like them better from f-droid.
Street Complete is an awesome way to contribute to OpenStreetMap.
Thunderbird (!) which is a fork of K9 (still active), and looks and runs great. Highly recommend.
I recently swapped from the F-Droid version of AntennaPod to the Google Play Store version so that I could use Chromecast, which they strip from their F-Droid builds because the underlying library isn't open-source and is deemed "impure" by F-Droid (it gets you a "This app has features you might not like" banner, when honestly it's a feature I specifically want).
A similar thing is true of Tempo (a Subsonic-client music player), where the F-Droid builds have Chromecast support stripped out, but the GitHub-published builds have it (so I also have to install Obtanium to get those updated).
"I want to listen to my audio on my devices in my house" is a weird thing to exclude in the name of open-source purity.
Otherwise, I love F-Droid. I just wish they had a bit more nuance to recognize that Chromecast support isn't the same as "constantly reports your location in the background to corporate servers", and so those shouldn't have the same severity of warning banners applied.
Great list, some of the apps I commonly use you did not mention:
Aves Libre (Gallery)
Breezy Weather (Weather overview)
Fossify Calendar
Immich (Self hosted Google Photos alternative)
K-9 Mail (E-Mail, to be rebranded to Thunderbird Mobile at some point in the future)
NetGuard (Firewall and logging)
Nextcloud (Self-hosted cloud storage)
Unexpected Keyboard (Keyboard that works nicely with Termux)
Librera FD (F-Droid) has OPDS stripped out.
https://github.com/foobnix/LibreraReader/issues/1335
But you can get the Play Store version through Obtainium. It's the PRO version (also available with Obtainium) the one with OPDS support.
It's super annoying though, that installing an app from F-Droid sometimes appears as installed from Play Store as well. For example, I have VLC installed from F-Droid, but it also appears in the Play Store update list and _can't_ be updated from there.
Does someone know why this is? I assume it's Google just assuming it's the only app source and not bothering to check the installation source associated with apps when pulling them into its update check list. Or is there no way on Android to check whether you're the one that installed an app?
Forkyz (collects crossword puzzles from different sources, like the New York Times)
PySolFc (mahjong, solitaire, other classic single-player games)
Shattered Pixel Dungeon
Dungeon Crawl Stone Soup
MTG Familiar (database of Magic the Gathering cards and rules)
Learning Japanese:
AnkiDroid
Kakugo (for kanji writing practice)
Miscellaneous:
NewPipe (buggy every so often, but it makes YouTube bearable for me)
OsmAnd~ (offline map and directions app)
SecScanQR (basic QR reader)
Vanilla Music
LibreOffice Viewer
MuPDF viewer
KeePassDX
Termux
In addition to all the other recommendations, Trail Sense is pretty great, and BRouter is quite useful for finding alternative routes if you use OsmAnd and cycle a lot.
I also use Etar and DAVx⁵ for calendar and contacts sync.
Rethink is useful if you don't already have another VPN setup for ad blocking etc.
I think I have maybe two apps installed via it currently. If something is available on the Google App Store I'm generally using that instead.