There is a way to make this work. It goes like this:
You do not use any external sync mechanism. Instead you work on one file only. Multiple clients can have it open simultaneously.
The apps I use succesfully that way are KeepassXC on Linux and Keepass2Android on Android.
You make the file accessible via SFTP (WebDAV might work too, although I haven’t tried that). I have a public server running where I created an account to only serve this keepass db file.
On the Linux clients I created an automount via SSHFS. KeepassXC opens the file via this mount.
Keepass2Android has SFTP built-in and can therefore access the file directly itself. This is important since all solutions that involve presenting the file via Android Storage Provider are not designed for that task and can lead to data loss (ask me how I know.) That’s why KeePassDX is not an option. It deals with local files only. (I haven’t checked any of the other Android apps.)
The syncing is handled by the apps themselves. They can detect or be made aware of changes to the file by the user that may happen even whilst they have it open, and they both handle the syncing correctly and reliably.
Keepass2Android can even deal with network outages since it is smart enough to keep an internal local copy of the file and to take care of the sync later.
Since KeepassXC doesn’t have this caching it needs the network to be up. You should create a cron job (or systemd timer) that makes a local copy every now and then, so you have a fallback.
There is a way to make this work. It goes like this: