Revert state DB injection and agent graph store (#21481)

## Why

Reverts #20689 to restore the previous optional state DB plumbing. The
conflict resolution keeps the newer installation ID and session/thread
identity changes that landed after #20689, while removing the mandatory
state DB and agent graph store dependency from ThreadManager
construction.

## What changed

- Restored `Option<StateDbHandle>` through app-server, MCP server,
prompt debug, and test entry points.
- Removed the `codex-core` dependency on `codex-agent-graph-store` and
reverted descendant lookup back to the existing state DB path when
available.
- Kept newer `installation_id` forwarding by passing it beside the
optional DB handle.
- Kept local thread-name updates working when the optional state DB
handle is absent.

## Validation

- `git diff --check`
- `cargo test -p codex-thread-store`
- `cargo test -p codex-state -p codex-rollout -p
codex-app-server-protocol`
- Attempted `env CARGO_INCREMENTAL=0 cargo test -p codex-core -p
codex-app-server -p codex-app-server-client -p codex-mcp-server -p
codex-thread-manager-sample -p codex-tui`; blocked locally by a rustc
ICE while compiling `v8 v146.4.0` with `rustc 1.93.0 (254b59607
2026-01-19)` on `aarch64-apple-darwin`.

codex-rs/core/src/session/session.rs

@@ -368,7 +368,6 @@ impl Session {
         agent_control: AgentControl,
         environment_manager: Arc<EnvironmentManager>,
         analytics_events_client: Option<AnalyticsEventsClient>,
-        state_db: Option<state_db::StateDbHandle>,
         thread_store: Arc<dyn ThreadStore>,
         parent_rollout_thread_trace: ThreadTraceContext,
     ) -> anyhow::Result<Arc<Self>> {
@@ -468,7 +467,22 @@ impl Session {
             otel.name = "session_init.thread_persistence",
             session_init.ephemeral = config.ephemeral,
         ));
-        let state_db_ctx = if config.ephemeral { None } else { state_db };
+        let state_db_fut = async {
+            if config.ephemeral {
+                None
+            } else if let Some(local_store) =
+                thread_store.as_any().downcast_ref::<LocalThreadStore>()
+            {
+                local_store.state_db().await
+            } else {
+                None
+            }
+        }
+        .instrument(info_span!(
+            "session_init.state_db",
+            otel.name = "session_init.state_db",
+            session_init.ephemeral = config.ephemeral,
+        ));
 
         let auth_manager_clone = Arc::clone(&auth_manager);
         let config_for_mcp = Arc::clone(&config);
@@ -492,8 +506,8 @@ impl Session {
         ));
 
         // Join all independent futures.
-        let (thread_persistence_result, (auth, mcp_servers, auth_statuses)) =
-            tokio::join!(thread_persistence_fut, auth_and_mcp_fut);
+        let (thread_persistence_result, state_db_ctx, (auth, mcp_servers, auth_statuses)) =
+            tokio::join!(thread_persistence_fut, state_db_fut, auth_and_mcp_fut);
 
         let mut live_thread_init =
             LiveThreadInitGuard::new(thread_persistence_result.map_err(|e| {