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/app-server/src/message_processor.rs

@@ -61,7 +61,6 @@ use codex_app_server_protocol::experimental_required_message;
 use codex_arg0::Arg0DispatchPaths;
 use codex_chatgpt::workspace_settings;
 use codex_core::ThreadManager;
-use codex_core::agent_graph_store_from_state_db;
 use codex_core::config::Config;
 use codex_core::thread_store_from_config;
 use codex_exec_server::EnvironmentManager;
@@ -255,7 +254,7 @@ pub(crate) struct MessageProcessorArgs {
     pub(crate) environment_manager: Arc<EnvironmentManager>,
     pub(crate) feedback: CodexFeedback,
     pub(crate) log_db: Option<LogDbLayer>,
-    pub(crate) state_db: StateDbHandle,
+    pub(crate) state_db: Option<StateDbHandle>,
     pub(crate) config_warnings: Vec<ConfigWarningNotification>,
     pub(crate) session_source: SessionSource,
     pub(crate) auth_manager: Arc<AuthManager>,
@@ -294,16 +293,14 @@ impl MessageProcessor {
         // affect per-thread behavior, but they must not move newly started,
         // resumed, or forked threads to a different persistence backend/root.
         let thread_store = thread_store_from_config(config.as_ref(), state_db.clone());
-        let agent_graph_store = agent_graph_store_from_state_db(state_db.clone());
         let thread_manager = Arc::new(ThreadManager::new(
             config.as_ref(),
             auth_manager.clone(),
             session_source,
             environment_manager,
             Some(analytics_events_client.clone()),
-            state_db.clone(),
             Arc::clone(&thread_store),
-            agent_graph_store.clone(),
+            state_db.clone(),
             installation_id,
         ));
         thread_manager
@@ -350,7 +347,7 @@ impl MessageProcessor {
             Arc::clone(&config),
             feedback,
             log_db,
-            Some(state_db.clone()),
+            state_db.clone(),
         );
         let git_processor = GitRequestProcessor::new();
         let initialize_processor = InitializeRequestProcessor::new(
@@ -400,7 +397,7 @@ impl MessageProcessor {
             thread_watch_manager.clone(),
             Arc::clone(&thread_list_state_permit),
             thread_goal_processor.clone(),
-            Some(state_db.clone()),
+            state_db.clone(),
         );
         let turn_processor = TurnRequestProcessor::new(
             auth_manager.clone(),