There is no such thing as “the password” – every user should have their own password. So, did you change the password of an administrative user? Of the WebDAV user (if there is a WebDAV user)?
Your password should be stored in either the macOS keychain or a password manager like 1Password. And it’s trivial to copy it from there.
Which raises the same question as before: Do you use a dedicated webDAV user? Did you change their password? Or another one?
The main disadvantage is that you have to mount the corresponding NAS volume. Probably manually. If you don’t, no sync will happen. With WebDAV, that is not necessary.
I doubt that there is any problem with WebDAV. If you set up your sync as described here, you’ll probably have a dedicated WebDAV user whose password you did not change.
But if all you’re using are two Macs that are in the same location, Bonjour might indeed be your best choice, as suggested by @DTLow