* NextCloud -- client for personal NextCloud server; this app is used primarily for file sync, with other features accessed with other apps. (https://nextcloud.com/features/?filter=Clients#android-clien...)
* KeePassDX -- password manager, shares DB with KeePassXC on desktop, which is synced via NextCloud. Also functions as a TOTP authenticator. (https://www.keepassdx.com/)
* DAVx5 -- CalDAV and CardDAV client; keeps mobile calendar and contact list synced with private NextCloud server. (https://www.davx5.com/)
* AntennaPod -- excellent FOSS podcatcher. (https://antennapod.org/)
* KDE Connect -- desktop sync tool; allows file/clipboard/keyboard/audio/etc. sharing between phone and a Linux desktop. (https://kdeconnect.kde.org/)
* Kore -- remote control app for a Kodi instance running on your LAN. (https://kodi.wiki/view/Kore)
And I don't see F-Droid itself mentioned -- it's the most popular repository of FOSS software for Android, with an accompanying app: https://f-droid.org.
F-Droid itself is great, but I find that the NeoStore front end to F-Droid is superior because it has multi-repository capability, offering a long list of alternative apk sources that can readily be verified for quality.