Remove `bringup: true` from realm_checker and remove the redundant tool test. (#137186)

Now that the realm checker is no longer in bringup, we can remove the tool test that checks for the empty realm file.

.ci.yaml

@@ -1100,7 +1100,6 @@ targets:
       - .ci.yaml
 
   - name: Linux realm_checker
-    bringup: true
     recipe: flutter/flutter_drone
     timeout: 60
     properties:

packages/flutter_tools/test/general.shard/cache_test.dart

@@ -356,15 +356,6 @@ void main() {
 
       expect(cache.storageBaseUrl, contains('flutter_archives_v2'));
     });
-
-    test('bin/internal/engine.realm is empty', () async {
-      final FileSystem fileSystem = globals.fs;
-      final String realmFilePath = fileSystem.path.join(
-        getFlutterRoot(), 'bin', 'internal', 'engine.realm');
-      final String realm = fileSystem.file(realmFilePath).readAsStringSync().trim();
-      expect(realm, isEmpty,
-        reason: 'The checked-in engine.realm file must be empty.');
-    });
   });
 
   testWithoutContext('flattenNameSubdirs', () {