Syncthing is probably the safest of all options, but if you want to trade a bit of paranoia for convenience, you can also sync your keepass database to a cloud provider of your choice. Then your pc doesnt have to be running to synchronize. As long as AES stays secure, even the cloud provider cannot decrypt it.

For added security, you can encrypt your password database with a file in addition to the master password (and then manually transfer that file to your phone via wire once).