Aurora Store - Anonymized frontend for Playstore
F-Droid - Open Source App Store
Obtainium - App Store for other sources (e.g. github)
Organic Maps - Open Source navigation (not as good as proprietary ones though)
SherpaTTS - Text to speech for Organic Maps
PDF Doc Scanner - Little Trickster, Open Source document scanner
Binary Eye - Barcode reader
K9 Mail / FairMail - Mail client
LocalSend - Cross Platform File Transfer
Syncthing Fork - Catfriend1 Syncthing fork to sync files
VLC Media Player - media player
KOReader - ebook reader
Voice - Paul Woitaschek, local audiobook player
AudioBookShelf - Remote audiobook player
Immich - image backup
Fossify File Manager - file manager
Substreamer / DSub - Audio streamer for navidrome self hosted server
OpenCamera - Open Source camera app
I wish I had this list from the start... Hope it helps someone :-)The only problems you might run into would be some features might require privileged access, things like Now Playing. Makes sense because normal apps cannot have unrestricted access to the microphone like that. Google Wallet works, but you cannot make payments because the app refuses to work on alternate OSes.
Besides that kind of stuff, though, I've used all sorts of Google apps without issues.