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/exec/src/lib.rs

@@ -478,6 +478,8 @@ pub async fn run_main(cli: Cli, arg0_paths: Arg0DispatchPaths) -> anyhow::Result
             None
         }
     };
+    codex_core::otel_init::record_process_start(otel.as_ref(), "codex_exec");
+    codex_core::otel_init::install_sqlite_telemetry(otel.as_ref(), "codex_exec");
 
     let otel_logger_layer = otel.as_ref().and_then(|o| o.logger_layer());