feat(core): add db health checks and provider interoperability

Add automated SQLite health diagnostics with optional auto-repair,
startup and scheduled execution, authenticated API routes, an MCP tool,
and dashboard visibility for status and repair actions.

Improve provider compatibility by adding Cursor usage fetching and
v3.1.0 parity headers, introducing a per-connection Codex Responses
store opt-in with session fallback, fixing Codex non-stream combo and
SSE translation behavior, sanitizing Gemini googleSearch tool payloads
and Qwen thinking tool_choice handling, and hardening cleanup and call
log storage paths.

tests/unit/executor-codex.test.mjs

@@ -130,6 +130,29 @@ test("CodexExecutor.transformRequest preserves compact requests and native passt
   assert.equal(result.instructions, "keep this");
 });
 
+test("CodexExecutor.transformRequest preserves store-enabled responses state when explicitly enabled", () => {
+  const executor = new CodexExecutor();
+  const body = {
+    _nativeCodexPassthrough: true,
+    _omnirouteResponsesStore: true,
+    instructions: "keep this",
+    previous_response_id: "resp_prev_123",
+    stream: false,
+  };
+
+  const result = executor.transformRequest("gpt-5.3-codex", body, false, {
+    requestEndpointPath: "/responses/compact",
+    providerSpecificData: {
+      openaiStoreEnabled: true,
+      requestDefaults: { serviceTier: "priority" },
+    },
+  });
+
+  assert.equal(result._omnirouteResponsesStore, undefined);
+  assert.equal(result.store, true);
+  assert.equal(result.previous_response_id, "resp_prev_123");
+});
+
 test("CodexExecutor.transformRequest applies per-connection reasoning and service tier defaults", () => {
   const executor = new CodexExecutor();
   const result = executor.transformRequest(