No personal knowledge of them but a couple would be sabre/dav and radicale:

• https://github.com/sabre-io/dav

• https://sabre.io/

• https://github.com/Kozea/Radicale

• https://radicale.org/v3.html

edit: and for Android phones the DAVx⁵ is a great caldav and carddav client
https://f-droid.org/packages/at.bitfire.davdroid/

How does that differ from Bitwarden?

On the other hand, using bitwarden might require some level of trust. How much should I trust the company to use the free service?
How do I know if my passwords would be safe, not being exposed to the wide net?

Wouldn’t these questions be as true of the VPS service that hosts Vaultwarden as of Bitwarden?
If my internet at home was better I would be selfhosting Vaultwarden and use a full vpn on my laptop/phone/tablet when leaving the house.
Now I’m using KeepassXC with my home pc as the true source and syncing copies of the database to my laptop and phone.