apps/entities: invalidate obs count cache on save, drop per-read stat
wire clear_observation_count_cache() into save_observations and _clear_merge_caches so the count cache invalidates on the same write paths as its sibling caches.
drop the Path.stat() / st_mtime_ns check from count_observations; warm reads now make zero syscalls, matching the four sibling caches in this module.
follow up dd5c0327 (apps/entities: warm caches and memoize obs counts on all-facets path).
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>