feat(FN-4135): add always-on web search with locked provider setting

Adds always-on web search capability to the research system, locking the web search provider in settings UI and updating the ResearchView to surface web search as a persistent toggle with agent tool integration, plus corresponding docs and test coverage.

Fusion-Task-Id: FN-4135

packages/cli/src/extension.ts

@@ -240,9 +240,7 @@ async function getResearchAvailability(store: TaskStore): Promise<{ ok: boolean;
   const backend = (resolved.searchProvider as string | undefined) ?? settings.researchGlobalWebSearchProvider ?? "builtin";
   const configured = backend === "builtin"
     ? true
-    : backend === "none"
-      ? false
-      : backend === "searxng"
+    : backend === "searxng"
         ? Boolean(settings.researchGlobalSearxngUrl)
         : backend === "brave"
           ? Boolean(settings.researchGlobalBraveApiKey)