Not desktop only, KeePass uses an encrypted file, all you need is a way to decrypt it. You can store it in iCloud or whatever you like to sync files between devices.

iOS has a good open source app KeeForge to open the encryped password files. I use SyncTrain on my phone to connect to my SyncThing network.

It's unfortunate that its a bit fragmented but there are Android / iOS complements as well - respectively keepassDX and keepassium.

There are several good Android Keepass clients, and Syncthing apps too.

Look longer :)