feat(cloud-agent): Cursor Cloud Agent via official REST API key (#4227) (#4250)

Integrated into release/v3.8.29 — Cursor Cloud Agent (cursor-cloud) via official api.cursor.com REST API key, 4th cloud agent mirroring Devin/Jules.

Pre-merge work done on the PR branch (fix-in-place):
- Wired cursor-cloud into the dashboard UI (CLOUD_AGENTS dropdown), health PROVIDER_NAMES, and lobeProviderIcons — it was API-usable but not selectable in the UI and rendered with the Jules fallback.
- Fixed cloud-agent-health-api.test.ts which asserted exactly 3 agents (the PR added a 4th) -> updated count/order + added cursor-cloud coverage.
- file-size baseline: page.tsx 913->922.

FOLLOW-UP (Rule #18): the REST endpoint paths/field names follow Cursor's documented Cloud Agents v0 API but still need a live validation run against a real Cursor API key. The integration is additive/opt-in and baseUrl is overridable per-credential, so any path/version correction needs no code change. Thanks @MRDGH2821 for the issue (#4227).

scripts/check/check-known-symbols.ts

@@ -440,6 +440,9 @@ export function extractCloudAgentRegistryKeys(registrySource: string): Set<strin
  */
 export const AGENT_FILE_TO_REGISTRY_KEY: Record<string, string> = {
   codex: "codex-cloud",
+  // #4227: file agents/cursor.ts ↔ registry key "cursor-cloud" (distinct from the
+  // OAuth chat provider `cursor`).
+  cursor: "cursor-cloud",
 };
 
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