I use KeePassium on iOS, synced with Dropbox. Works perfectly. Other sync methods are available too.

I have been enjoying Strongbox for passwords plus Mobius Sync (a Syncthing implementation) to keep the password file synced. I am on iOS.

Mobius Sync can sync a file to iOS’ built in file store, and Strongbox can read that. So they work pretty well as a pair.

Is there now a straightforward way (on both platforms) to use KeePassXC in the role of login keyring/keychain? Last time I looked, admittedly not recently, the answer was “we think you shouldn't want this”.

I don't know, I do everything manually. I remember most of my passwords, but when I forget one I open KeePassXC and copy-paste the pwd into the login. And once every month or so, I'll manually ship the databases around in round-robin manner and to update them on every machine. Mainly b/c my pwd database is one thing I don't really want to trust to the cloud, and the manual effort of not doing that isn't too onerous.

I can also recommend using Syncthing for a cloud-less synchronization between the machines

KeePassDX on Android

KeePass2Android is great (for Android) - been using for 5+ years