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 :-)Some apps require Google's FCM for push notifications. You need to install Sandboxed Google Play services from the GrapheneOS App Store and grant them unrestricted battery access (so they can run in the background, which is required for maintaining a network connection to FCM and delivering notifications). https://grapheneos.org/faq#notifications
Other apps like Signal use their own background connections, for example WebSockets, to deliver push notifications, but keeping a connection open for each app consumes more battery life than just having one background network connection. Also, not every app supports this.
For Signal specifically, the GrapheneOS project recommends either using FCM via Sandboxed Google Play, or installing Molly (https://molly.im/), a fork of the Signal client for Android, which makes some changes to reduce battery consumption when using WebSocket-based notifications. It also allows you to use UnifiedPush (https://unifiedpush.org/) for notifications instead, but that requires an application called mollysocket (https://github.com/mollyim/mollysocket) running on a server.