feat(relay): add early startup lifecycle telemetry

Record typed process-entry phases through metrics readiness, make metrics installation and exporter lifetime explicit, and cover production failure, secrecy, scrape, and teardown paths.

Refs #7238.

Co-authored-by: Ravneet Arora <rarora@squareup.com>
Signed-off-by: Ravneet Arora <rarora@squareup.com>

Author: ravarora2

crates/buzz-relay/src/lib.rs

@@ -25,6 +25,8 @@ pub mod error;
 pub mod handlers;
 /// Stateless HMAC-signed relay invite tokens (mint/verify).
 pub mod invite_token;
+/// Typed process-startup lifecycle events and terminal accounting.
+pub mod lifecycle;
 /// Inter-relay mesh startup wiring (`BUZZ_MESH` seam).
 pub mod mesh_boot;
 /// Prometheus metrics: recorder, upkeep, HTTP middleware.