perf(api,frontend): index hot queries, paginate chats, fix realtime

backend/src/utils/cache.py

@@ -0,0 +1,4 @@
+IMMUTABLE_HEADERS = {"Cache-Control": "public, max-age=31536000, immutable"}
+DAY_HEADERS = {"Cache-Control": "public, max-age=86400"}
+SHORT_HEADERS = {"Cache-Control": "public, max-age=300"}
+NO_STORE_HEADERS = {"Cache-Control": "no-cache"}