* 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/)
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.
Neo Store looks interesting, but the readme in the GitHub repo includes emojis in the feature list, which is a bit of a red flag for me, especially since the project appears to have started only two years ago.
* 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.