Rewrite PackageWatchdogTest#testRegistration (3/n)

Following go/unit-test-practices, we split testRegistration into smaller
ones so each test focuses on one behavior at a time.

Note we will remove testRegistration in a later CL.

Bug: 140472424
Test: atest PackageWatchdogTest
Change-Id: I88e00a8fc43b953d575ee047979b7fe1d5fbd3ba