Currenly goose is using jackc/pgx driver to connect to PostgreSQL databases (https://github.com/pressly/goose/blob/main/cmd/goose/driver_postgres.go), but I dont see any option to connect to them using Kerberos.
There is also add-in third-party feature that enables GSSAPI/Kerberos authentication via that driver - https://github.com/otan/gopgkrb5. Also, the author of pgx mentioned that library in his project (https://github.com/jackc/pgx?tab=readme-ov-file#githubcomotangopgkrb5).
Maybe it should be added to cover more cases with authentication? Looks like it cannot be achieved only via providing gssencmode=require in PostgreSQL connection string.