Google searching almost never brings me up information. ....Never in 5 years, have I heard about UID and GID.
That's part of the problem! I've expressed before to limit this 'info exposure' and make sure it's current. Old info leads to many wild goose chases.
Anymore google (or any SE) is my LAST resort. Man pages and other published help is better, and maybe on your system already! Much of the time I find a how-to before I read the concerning documentation I go on a unfruitful tangent.
Anyway, the user info and extended attributes in linux are really intended to be 'local' and not 'global' I use the term 'foreign' disc for your backup because that's what it is, and the user info does not relate to the system its mounted on though the local system will translate user id to the local users, and as a result will LIE! I mentioned user 1003, well, move his data to that other computer that also has a user 1003 and now all that data is owned by Sue and not Bob. You may even find files with 100x as the owner and no translation to a user name. So mount Bob's disc on a machine with no user 1003, it will show only 1003 and not 'Bob'.
The common group method does work. This common group does not need to be a 'user', just a group that owns the data. Make your users members of that group. If your backup disc is owned by the 'backup' group, then each new system you create, add it's user (1000) to the 'backup' group.
Also you could consider not using any file based backups. Archives (zip, et al) can package with and without user info. Full disk images are convenient.
Overall it's a poor setup and susceptible to mixing itself up, so I ignore the specifics, since it's BS. Just make sure to use a distro with some functional root and you can always get around the 'obfuscation' and realize it's NOT security.