[flutter_tools] normalize windows file path cases in flutter validator (#115889)

* normalize windows file path cases in flutter validator

* fix

* make comparison more accurate by checking .startsWith() rather than .contains()

* fix method name

* call path.canonicalize

* fix

packages/flutter_tools/lib/src/doctor.dart

@@ -619,7 +619,7 @@ class FlutterValidator extends DoctorValidator {
       );
     }
     final String resolvedFlutterPath = flutterBin.resolveSymbolicLinksSync();
-    if (!resolvedFlutterPath.contains(flutterRoot)) {
+    if (!_filePathContainsDirPath(flutterRoot, resolvedFlutterPath)) {
       final String hint = 'Warning: `$binary` on your path resolves to '
           '$resolvedFlutterPath, which is not inside your current Flutter '
           'SDK checkout at $flutterRoot. Consider adding $flutterBinDir to '
@@ -629,6 +629,13 @@ class FlutterValidator extends DoctorValidator {
     return null;
   }
 
+  bool _filePathContainsDirPath(String directory, String file) {
+    // calling .canonicalize() will normalize for alphabetic case and path
+    // separators
+    return (_fileSystem.path.canonicalize(file))
+        .startsWith(_fileSystem.path.canonicalize(directory) + _fileSystem.path.separator);
+  }
+
   ValidationMessage _getFlutterUpstreamMessage(FlutterVersion version) {
     final String? repositoryUrl = version.repositoryUrl;
     final VersionCheckError? upstreamValidationError = VersionUpstreamValidator(version: version, platform: _platform).run();