chore: remove dead code, deprecate unused plugin APIs (over-engineering audit)

Whole-tree audit. Every symbol was checked against core, the plugin
monorepo and all eight third-party plugins in plugins.json first.

- Deprecate (removal 3.10.0) plugin-facing methods nothing calls:
  LogoDownloader bulk download, ConfigManager backup/secret wrappers,
  APIHelper extras, BackgroundDataService poll API, PluginManager /
  PluginStateManager info readers, and a few CacheManager, FontManager,
  BaseOddsManager, DynamicTeamResolver methods and PluginTestCase.
  plugin_api_usage.py learns their receiver names; DEPRECATIONS doc
  regenerated.
- Remove core-internal dead code: CacheMetrics, Vegas status/stats
  plumbing, sync "new cycle" message (followers ignore unknown types),
  unused operation types, test-only PluginCatalog readers, IPC to_dict
  and ping, _parse_form_value, CacheStrategyProtocol, ErrorAggregator
  callbacks, duplicate web response helpers.
- Web UI: drop never-mounted json-file-manager.js, the example widget,
  utils/error_handler.js, four uncalled PluginAPI methods, and 29
  escapeHtml shims (call window.LEDEscape directly). Public globals,
  BaseWidget and widget names unchanged.
- Remove six one-off scripts (owner decision) and the unused markupsafe
  and pytest-mock pins.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

test/test_vegas_static_mode.py

@@ -52,9 +52,6 @@ class FakeStream:
     def get_static_layout(self):
         return [(pid, w is None) for pid, w in self.layout]
 
-    def get_active_plugin_ids(self):
-        return [pid for pid, _ in self.layout]
-
     def is_static_plugin(self, plugin_id):
         return plugin_id in self.statics
 
@@ -163,7 +160,6 @@ class TestStreamManagerSkipsStaticContent:
         sm.plugin_manager = SimpleNamespace(plugins=plugins)
         sm.plugin_adapter = MagicMock()
         sm.plugin_adapter.get_content.return_value = [block(10)]
-        sm.stats = {'segments_fetched': 0, 'fetch_errors': 0}
         sm.refresh = lambda: None
         return sm
 
@@ -213,7 +209,6 @@ class TestCoordinatorStaticPause:
         coord._live_priority_active = False
         coord._live_priority_check = None
         coord._interrupt_check = None
-        coord.stats = {'static_pauses': 0}
         return coord
 
     def _plugin(self):