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_coordinator_iteration.py

@@ -27,7 +27,6 @@ def _coordinator(plugins):
     coord.stream_manager = MagicMock()
     coord.display_manager = MagicMock()
     coord.plugin_manager = SimpleNamespace(plugins=plugins, get_plugin=plugins.get)
-    coord.stats = {'cycles_completed': 0, 'interruptions': 0}
     coord._state_lock = threading.Lock()
     coord._is_active = True
     coord._is_paused = False
@@ -99,7 +98,6 @@ def test_vegas_resumes_after_a_live_priority_pause():
 
 def test_stop_clears_a_live_priority_pause():
     coord = _live_coordinator(['nfl_live'])
-    coord._start_time = None
     coord._restore_switch_interval = lambda: None
     coord._remove_render_gate = lambda: None
     coord.run_iteration()