The database/sql package gained native support[1] for the uuid.UUID type so it will Just Work even without the methods. This probably should have been mentioned in the release notes and database/sql package docs.
Repeating the package name is fine if it's exactly the same name (modulo capitalization) and there's nothing better to name the type anyway. The style issue would arise with e.g. uuid.UUIDVersion, which should just be named uuid.Version. There used to be a gopls lint that would flag names like uuid.UUID but it got relaxed awhile ago.
[1] https://cs.opensource.google/go/go/+/refs/tags/go1.27.0:src/...