docs: update project docs for warm start and chain health check

Add warm start and chain pre-flight sections to USAGE. Mark both
features complete in ROADMAP and TASKS. Remove implemented items
from TODO. Update README, PROJECT, and CHEATSHEET.

docs/USAGE.md

@@ -131,6 +131,11 @@ Each cycle tests all proxies through the full chain (static chain + proxy)
 by sending an HTTP GET to `test_url`. Proxies are marked alive on `200` response.
 After `max_fails` consecutive failures, a proxy is evicted.
 
+Before each health test cycle, the static chain is tested without any pool
+proxy. If the chain itself is unreachable (e.g., Tor is down), proxy tests
+are skipped entirely and a warning is logged. This prevents false mass-failure
+and unnecessary evictions.
+
 Mass-failure guard: if >90% of tests fail in one cycle, eviction is skipped
 (likely the static chain is broken, not the proxies).
 
@@ -167,6 +172,14 @@ Pool state is saved to `state_file` (default: `~/.cache/s5p/pool.json`) after
 each refresh/health cycle and on shutdown. On startup, previously-alive proxies
 are loaded for fast warm starts.
 
+### Warm start
+
+When restarting with an existing state file, only the previously-alive proxies
+are tested before the server starts accepting connections. A full health test
+of all proxies runs in the background. This reduces startup blocking from
+minutes to seconds on warm restarts. Cold starts (no state file) test all
+proxies before serving.
+
 ### CLI shorthand
 
 ```bash