Add process-scoped SQLite telemetry (#22154)

## Summary
- add SQLite init, backfill-gate, and fallback telemetry without
introducing a cross-cutting state-db access wrapper
- install one process-scoped telemetry sink after OTEL startup and let
low-level state/rollout paths emit through it directly
- add process-start metrics for the process owners that initialize
SQLite

---------

Co-authored-by: Owen Lin <owen@openai.com>

codex-rs/mcp-server/src/message_processor.rs

@@ -5,7 +5,6 @@ use codex_arg0::Arg0DispatchPaths;
 use codex_core::StateDbHandle;
 use codex_core::ThreadManager;
 use codex_core::config::Config;
-use codex_core::thread_store_from_config;
 use codex_exec_server::EnvironmentManager;
 use codex_extension_api::empty_extension_registry;
 use codex_login::AuthManager;
@@ -71,7 +70,7 @@ impl MessageProcessor {
             environment_manager,
             empty_extension_registry(),
             /*analytics_events_client*/ None,
-            thread_store_from_config(config.as_ref(), state_db.clone()),
+            codex_core::thread_store_from_config(config.as_ref(), state_db.clone()),
             state_db.clone(),
             installation_id,
             /*attestation_provider*/ None,