Do I need to be on the latest version of macOS for Apple Store repair?
Solution 1:
No, they should not require you to update.
However, even if they do (such as if they damage the machine and have to wipe it for some unforeseen reason) a backup can still be restored to Mojave.
There is no restriction to prevent you from restoring your computer to an earlier version, so long as it is compatible with that version.