There are a few decent Android and iOS apps that work well. I use Nextcloud and WebDAV for access.
Not a setup I can recommend to just anybody though.
The need to have an opinion on how you’d like to sync a file does, as you suggest, eliminate some portion of the population who need a fully baked answer in one step.
I used to use Google Drive, but now I use Syncthing, further reducing my exposure. Paired with Synctrain and KeePassium on iOS.
One tip: enable the atomic save option in settings to reduce the risk of weird cloud sync issues.
For syncing, I do it manually with rsync. Given the database is 1 file it's easy to move around. You can rsync / scp it over, use a USB cable, use cloud storage, etc..
I use a password manager in a "read many, write infrequently" way so I don't mind occasionally syncing it as needed.
I’m sure it works for many people to Dropbox their vault around anytime they want to access something and manually handle copies and sync. I’m not nearly so naive as to think that has any degree of success outside tech bubbled people.
Bob: Why not just use $nerdware?
Alice: How does it solve $common_problem?
Bob: Well, it doesn't. $common_problem isn't really real, you see. You actually have $x and $y, and then there's $p and $q, and you just have to $x the $y and $p the $q and then it's almost as good. It's pretty much the same. It's even better, really.
Alice: I don't know about all that. But, I have $common_problem so I use the $common_software. It's just stupid sometimes.
Bob: So, why not just use $nerdware?