Get rid of custom ExceptionRule methods

The only remaining methods on ExceptionRule after this are methods that
also exist on ExpectedException, which will allow us to, in the next CL,
swap out the one for the other and then run the automated refactoring to
turn it all into assertThrows/expectThrows.

Note that there were some assertions about root causes that couldn't
easily be turned into ExpectedException invocations, so I simply
converted them directly to usages of assertThrows/expectThrows.

-------------
Created by MOE: https://github.com/google/moe
MOE_MIGRATED_REVID=178623431

javatests/google/registry/storage/drive/DriveConnectionTest.java

@@ -215,8 +215,8 @@ public class DriveConnectionTest {
           new ChildReference().setId("id2")))
       .setNextPageToken(null);
     when(childrenList.execute()).thenReturn(childList);
-    thrown.expect(IllegalStateException.class,
-        "Could not update file 'title' in Drive folder id 'driveFolderId' "
+    thrown.expect(IllegalStateException.class);
+    thrown.expectMessage("Could not update file 'title' in Drive folder id 'driveFolderId' "
             + "because multiple files with that name already exist.");
     driveConnection.createOrUpdateFile("title", MediaType.WEBM_VIDEO, "driveFolderId", DATA);
   }