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_live_integration.py

@@ -189,7 +189,7 @@ def test_with_live_refresh_off_the_same_run_is_plain_content(dm, tmp_path, ticke
     start_width = pipeline.scroll_helper.total_scroll_width
     assert _run_until(
         coordinator,
-        lambda: pipeline.stats.get('extensions', 0) >= 1, seconds=10.0)
+        lambda: pipeline.extensions >= 1, seconds=10.0)
     assert pipeline.live_records() == ()
     assert np.asarray(pipeline.scroll_helper.cached_array).shape[1] > 0
     assert start_width > 0