Add process-scoped SQLite telemetry

[jif-oai]

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

Notes

• equivalent telemetry surface to Add SQLite init and fallback telemetry #21632, but 22 files / 556 additions instead of the current 99 files / 2,530 additions

Test plan

• RUST_MIN_STACK=33554432 cargo test -p codex-state -p codex-rollout -p codex-thread-store -p codex-otel
• RUST_MIN_STACK=33554432 cargo test -p codex-app-server --lib
• RUST_MIN_STACK=33554432 cargo test -p codex-mcp-server --lib
• RUST_MIN_STACK=33554432 cargo test -p codex-tui --lib
• cargo check -p codex-state -p codex-rollout -p codex-thread-store -p codex-core -p codex-app-server -p codex-app-server-client -p codex-exec -p codex-tui -p codex-mcp-server
• just fix -p codex-state -p codex-rollout -p codex-otel -p codex-core -p codex-app-server -p codex-exec -p codex-mcp-server -p codex-tui
• just fmt

Known unrelated local failures:

• codex-exec::tests::thread_start_params_include_review_policy_when_review_policy_is_manual_only fails the same way on untouched main
• broader app-server integration tests fail in this sandbox because sandbox-exec cannot apply the profile here