[Perf] Cache API key validation to eliminate per-request MongoDB hit

[ishaanxgupta]

Description
Every authenticated request triggers a MongoDB find_one + update_one round-trip to validate the API key and update last_used. This is the single biggest latency contributor for authenticated endpoints, adding roughly 30–80ms to every request.

Code Reference
src/database/api_key_store.py - validate_api_key()

Proposed Fix
Add an in-memory TTL cache (e.g. cachetools.TTLCache) keyed by key_hash.
Cache validated results for 60–300s.
Batch last_used updates in a background task instead of blocking the main request path.