feat(telemetry): add headroom_stack and install_mode identity fields

Adds two orthogonal identity fields to the anonymous telemetry beacon so we
can segment usage by integration surface and deployment shape:

- headroom_stack: how Headroom is invoked (proxy, wrap_claude, wrap_codex,
  adapter_ts_openai, adapter_ts_anthropic, etc.). Resolved from HEADROOM_STACK
  env, HEADROOM_AGENT_TYPE fallback, or aggregated request-header counts.
- install_mode: how the proxy is deployed (wrapped / persistent / on_demand).
  Detected from HEADROOM_AGENT_TYPE plus DeploymentManifest lookup.

TS SDK adapters now tag every request with X-Headroom-Stack; a FastAPI
middleware buckets the counts and surfaces them via /stats so the beacon can
report requests_by_stack for mixed-integration sessions.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

sql/create_proxy_telemetry_v2.sql

@@ -15,6 +15,9 @@ CREATE TABLE IF NOT EXISTS proxy_telemetry_v2 (
     sdk text,
     backend text,
     session_minutes integer,
+    headroom_stack text,
+    install_mode text,
+    requests_by_stack jsonb,
 
     -- Effectiveness metrics
     tokens_saved bigint,