Syncthing is great. Servers are overrated anyway, I would rather everything be peer-to-peer wherever possible. Currently working on a script to integrate calcurse with DecSyncCC so I can keep my calendar synced between my laptop and phone without a server!
I keep mine in the cloud bit I also have a key file attached to it. That is not kept in the cloud so at least I have some security if the cloud service gets hacked and my password is 57 characters long.
There are two advantages of using the cloud for the database while keeping a key file out of it.
It's a backup that's not on any of your own devices.
Your devices sync with little effort. Save the file on one device, and the others have the new database automatically (when using common cloud storage providers that sync)
Understandable. I don't go very many places so this way is most convenient for me. For your situation I'm not real sure what would be the best practice for you, but I will be keeping an eye on this thread if someone has a better answer
I use KeePass and keep my database in the cloud. I use a key file that is never stored in the cloud in addition to my master password. You get a cloud backup of your database, and updates will sync to your devices if your cloud provider has a client that does that.
I actually don't sync it directly to my phone. I download a copy as needed. I also don't add passwords on my phone to my main database. I use a separate database for logins I create on my phone and import them once in a while on my PC. This is because Google Drive's sync on Android has been unreliable for me, though I haven't tried again in years.
I use KeePass DX on Android because it has a nice virtual keyboard so you don't have to use the clipboard, which is insecure. It also has a better UI with fingerprint unlocking.
Does it have to be in "the cloud" or just accessible multiple places? I have a nextcloud instance running that's locked down but allows sharing with my android phone. For other computers it's on a network share and if off site I can connect over Wireguard to my home network to get access.