I worry about this too. I store the database itself in Dropbox, and I also use a keyfile alongside the password to open it. I can easily recreate the keyfile on any computer, but it never goes anywhere near the internet.

In addition to that, for my really critical "gatekeeper" accounts, I don't put the full password in the database. Just a reminder that this is a "special" password, which needs to be combined with another bit of info in order to work.

I just live with the fact that I can't use this system on my phone, and for my usage patterns, that's fine. There's nothing I need to do that's so urgent that it can't wait until I'm back in front of my computer.

On my laptop. I synch to my phone and tablet using Syncthing. I write into the file only on the laptop.

I keep my db in my own freenas box and sync it between devices using resilio sync.