... and good alternatives, where available. To the best of my knowledge, and no guarantees obviously. All the apps listed here are distributed with libre licences (except where otherwise stated), but some may rely on non-libre backends.

Productivity

• DAVx5 - the easiest way to synchronize your Nextcloud contacts/calendar/tasks with corresponding Android apps. GPLv3. Available on F-Droid.
• K-9 Mail, or these days it is perhaps just as well to use Thunderbird for Android.
• Nextcloud
• Nextcloud Notes
• Tasks.org - a great tasks app that synchronizes with your Nextcloud tasks.

Chat, messaging

• Signal messenger. The app is FOSS, but relies on a proprietary and centralized service.
• Nextcloud Talk
• Beeper

Keyboard

• Unexpected Keyboard, F-Droid - keyboard with a smart swipe-inside-each-key UX that exposes a massive amount of special characters in a smart way.
• HeliBoard, F-Droid
• https://github.com/futo-org/android-keyboard
• Thumb-Key - cool keyboard meant for thumb typing and swiping inside each key.

Audio & video

• Audio Recorder, F-Droid. Easy to integrate with Nextcloud's "Auto Uploads" functionality, in my experience. But the default quality settings (bitrate, etc.) are quite low and I suggest raising them.
• Jellyfin, F-Droid - mobile client for Jellyfin media server.
• NewPipe, F-Droid - I recommend you install it on F-Droid using their repo to get updates faster (but note that this means you trust their repo to push updates to your phone).
• Tempo - music client for Subsonic-compatible servers.
• VLC

Misc

• Binary Eye, F-Droid - a competent QR code scanner.
• FreeOTP+, F-Droid - 2FA authenticator.
• Kvaesitso launcher - it looks great by default and can be customized in lots of useful ways.
• Librera Reader, F-Droid.
• OpenKeychain - in combination with Password Store to sync pass to Android.
• OsmAnd - OpenStreetmap for Android.
• Tailscale - app is FOSS, but the underlying service is proprietary, but can replaced with Headscale (but unfortunately I cannot recommend it - tried it once and never figured it out).
• Transdroid - Bittorrent client that lets your monitor and control your server.
• Transportr - public transport timetables. Works well in Stockholm.
• Tusky - Mastodon client that works well with multiple accounts across different instances.
• Wallabag