The file syncing, particularly between Android phone and multiple desktop machines, is my biggest worry with this workflow. Will the synced Keepass file get corrupted if I add a new password on the phone and also on desktop, and then later try to merge them?

Been using this setup for many years and never had any problem at all. I sync between desktop and mobile with Syncthing[0]. You can configure Syncthing to do file versioning, it has many options (Trash Can, Simple, Staggered or External file versioning) so if some weird conflict happens you'll never lose data. But honestly, I have never had any issues, and I have been running this setup for many years. So I'm sure I have run into all kind of edge cases and it just works.

As side note, Syncthing is an amazing piece of software. I sync everything for my other devices into a central PC and from there I do the backups.

- [0]: https://syncthing.net/

No, KeepassXC has an option to merge databases, it never caused me any trouble. I have a similar setup to parent commenter.