feat(problems): surface stale supporter-binary pins (T-495)

The Problems panel flags a configured tool path (app.tools) that no longer
points at a file — a real misconfig, echoing D-58's soft floor. A merely-
unfound optional tool isn't flagged (its use-time userError covers that).
Extracted to a pure supporterToolProblems(), flutter-tested (3 cases).

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

test/builtin/problems/problems_controller_test.dart

@@ -0,0 +1,24 @@
+import 'package:clide/builtin/problems/src/problems_controller.dart';
+import 'package:clide/src/env/supporter_binaries.dart';
+import 'package:flutter_test/flutter_test.dart';
+
+void main() {
+  group('supporterToolProblems', () {
+    test('flags a stale supporter-binary pin', () {
+      final tools = SupporterBinaries(overrides: {'d2': '/gone/d2'}, exists: (_) => false);
+      final ps = supporterToolProblems(tools);
+      expect(ps.single.source, 'tools');
+      expect(ps.single.message, contains('d2'));
+      expect(ps.single.hint, isNotNull);
+    });
+
+    test('no problem when the configured path resolves', () {
+      expect(supporterToolProblems(SupporterBinaries(overrides: {'d2': '/ok'}, exists: {'/ok'}.contains)), isEmpty);
+    });
+
+    test('no problem with no override or no resolver', () {
+      expect(supporterToolProblems(SupporterBinaries(exists: (_) => false)), isEmpty);
+      expect(supporterToolProblems(null), isEmpty);
+    });
+  });
+}