feat(vegas): one declared participation per plugin (scroll | pause | exclude) (#682)

A plugin takes part in Vegas mode in one declared way: 'scroll', 'pause'
or 'exclude', resolved from the user's vegas_participation setting, the
manifest field, then the legacy hooks, so no plugin changes behaviour.
The stream manager decides inclusion and pauses through it; the installed
plugins API and the Vegas plugin-order list report it. Deprecates
get_supported_vegas_modes, get_vegas_segment_width and vegas_panel_count
for removal in 3.9.0, and regenerates docs/DEPRECATIONS_3.8.md to include
them.

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

web_interface/blueprints/api_v3/plugins.py

@@ -10,6 +10,9 @@ from web_interface.blueprints.api_v3 import (
     jsonify, logger, os, request, subprocess, success_response,
 )
 from src.common.path_safety import safe_path_component
+from src.plugin_system.base_plugin import (
+    configured_vegas_participation, resolve_vegas_participation,
+)
 import web_interface.blueprints.api_v3 as _pkg
 # Read through the module rather than bound by value: tests patch these
 # as module attributes, and a value binding would not see the patch.
@@ -129,6 +132,14 @@ def get_installed_plugins():
         if 'vegas_mode' in plugin_config:
             vegas_mode = plugin_config['vegas_mode']
 
+        # What Vegas actually does with the plugin: 'scroll', 'pause' or
+        # 'exclude'. The same resolution the ticker uses; without a loaded
+        # instance only the user's own setting is known.
+        if plugin_instance is not None:
+            vegas_participation = resolve_vegas_participation(plugin_instance, plugin_id)
+        else:
+            vegas_participation = configured_vegas_participation(plugin_id, plugin_config)
+
         return {
             'id': plugin_id,
             'name': plugin_info.get('name', plugin_id),
@@ -154,6 +165,7 @@ def get_installed_plugins():
             'web_ui_actions': plugin_info.get('web_ui_actions', []),
             'vegas_mode': vegas_mode,
             'vegas_content_type': vegas_content_type,
+            'vegas_participation': vegas_participation,
         }
 
     from concurrent.futures import ThreadPoolExecutor