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,

sql/upgrade_telemetry_stack_context.sql

@@ -0,0 +1,15 @@
+-- Add deployment-context columns to proxy_telemetry_v2
+-- Run in Supabase SQL Editor.
+--
+-- headroom_stack:      how Headroom is being invoked — e.g. "proxy",
+--                      "wrap_claude", "adapter_ts_openai", "mixed", "unknown".
+-- install_mode:        how the proxy process is deployed — one of
+--                      "wrapped", "persistent", "on_demand", "unknown".
+-- requests_by_stack:   JSONB dict {stack_slug: count} for sessions that see
+--                      multiple integration surfaces (e.g. a persistent proxy
+--                      serving both wrap_claude and TS adapter callers).
+
+ALTER TABLE proxy_telemetry_v2
+  ADD COLUMN IF NOT EXISTS headroom_stack text,
+  ADD COLUMN IF NOT EXISTS install_mode text,
+  ADD COLUMN IF NOT EXISTS requests_by_stack jsonb;