I transfer the database, keyfile, and exe files to the new target, then login. Or I might just hand-type the random-string, viewed from my phone, because I am a hardcore operations administrator. In the event of a catastrophic loss of access, I retain backup codes physically recorded in a safe location. And the keyfile, database, & exe are currently in 3 separate devices of mine.
All 3 PCs are in one location, as I only have one living location and rent no colo or VMs. But I'm not worried about having some sort of Dropbox access issue at the same time as a physical incident at my residence, as the probability is (I think) still lower than my very low risk avoidance.
Also not the GP, I do the same thing. In my case I need access to one of my devices with Dropbox configured (my laptop or my phone are most likely, my server syncs too)
Dropbox stores the files locally (on the phone, the kdbx file is marked to be cached and updated offline and I use dropsync)
If someone deletes my kdbx file from my Dropbox account, and I don't realize this in time (before all my devices sync _and_ my backups run out, so very small chance given the nature of the file) I'm in a lot of trouble...
Not the GP, but the password manager's database is likely setup as a Dropbox app. So when you login to your password manager, it retrieves the latest copy of the database. I do this with KeeWeb (cross platform PW manager compatible with KeePass database, although KeePass is better on Windows because of autotype).
