Reapply "[Github] Update PR labeller to v6.0.1 (#167246)"

This reverts commit b3d6264.

This broke the workflow because the sync-labels flag was set to a
zero-length string to work around an issue. The underlying issue has
been fixed and the value is now required to be a boolean. We can just
drop the value because we want the default behavior anyways. This should
be the last remaining breaking change from v5 that we need to migrate.

Author: boomanaiden154