Remove usage of --enable-experiment to analysis server (#69614)

packages/flutter/test_private/analysis_options.yaml

+include: ../analysis_options.yaml

packages/flutter/test_private/bin/test_private.dart

@@ -207,7 +207,7 @@ class TestCase {
       printOutputDefault: true,
     );
     final ProcessRunnerResult result = await runner.runProcess(
-      <String>[flutter, 'analyze', '--current-package', '--enable-experiment=non-nullable', '--pub', '--congratulate', '.'],
+      <String>[flutter, 'analyze', '--current-package', '--pub', '--congratulate', '.'],
       failOk: true,
     );
     if (result.exitCode != 0) {

packages/flutter_tools/test/commands.shard/permeable/analyze_once_test.dart

@@ -349,33 +349,6 @@ StringBuffer bar = StringBuffer('baz');
     }
   });
 
-  testUsingContext('analyze once supports analyzing null-safe code', () async {
-    const String contents = '''
-int? bar;
-''';
-    final Directory tempDir = fileSystem.systemTempDirectory.createTempSync('flutter_analyze_once_test_null_safety.');
-    _createDotPackages(tempDir.path, true);
-
-    tempDir.childFile('main.dart').writeAsStringSync(contents);
-    try {
-      await runCommand(
-        command: AnalyzeCommand(
-          workingDirectory: fileSystem.directory(tempDir),
-          platform: _kNoColorTerminalPlatform,
-          fileSystem: fileSystem,
-          logger: logger,
-          processManager: processManager,
-          terminal: terminal,
-          artifacts: artifacts,
-        ),
-        arguments: <String>['analyze', '--no-pub', '--enable-experiment=non-nullable'],
-        statusTextContains: <String>['No issues found!'],
-      );
-    } finally {
-      tryToDelete(tempDir);
-    }
-  });
-
   testUsingContext('analyze once returns no issues for todo comments', () async {
     const String contents = '''
 // TODO(foobar):