[daily] route codex websocket through site api endpoints (#386)

* fix: route codex websocket through site api endpoints

* fix: preserve websocket endpoint exhaustion errors

* test: align proxy route mocks with first-byte timeout helpers

src/server/routes/api/checkin.lock.test.ts

@@ -35,6 +35,7 @@ vi.mock('../../db/index.js', () => {
       insert: () => insertChain,
       select: () => queryChain,
     },
+    hasProxyLogStreamTimingColumns: async () => false,
     schema: {
       settings: { key: 'key' },
       checkinLogs: { accountId: 'accountId', createdAt: 'createdAt' },