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/test_support.rs

@@ -52,14 +52,14 @@ pub fn auth_manager_from_auth_with_home(auth: CodexAuth, codex_home: PathBuf) ->
     AuthManager::from_auth_for_testing_with_home(auth, codex_home)
 }
 
-pub async fn thread_manager_with_models_provider(
+pub fn thread_manager_with_models_provider(
     auth: CodexAuth,
     provider: ModelProviderInfo,
 ) -> ThreadManager {
-    ThreadManager::with_models_provider_for_tests(auth, provider).await
+    ThreadManager::with_models_provider_for_tests(auth, provider)
 }
 
-pub async fn thread_manager_with_models_provider_and_home(
+pub fn thread_manager_with_models_provider_and_home(
     auth: CodexAuth,
     provider: ModelProviderInfo,
     codex_home: PathBuf,
@@ -71,7 +71,22 @@ pub async fn thread_manager_with_models_provider_and_home(
         codex_home,
         environment_manager,
     )
-    .await
+}
+
+pub fn thread_manager_with_models_provider_home_and_state(
+    auth: CodexAuth,
+    provider: ModelProviderInfo,
+    codex_home: PathBuf,
+    environment_manager: Arc<EnvironmentManager>,
+    state_db: Option<crate::StateDbHandle>,
+) -> ThreadManager {
+    ThreadManager::with_models_provider_home_and_state_for_tests(
+        auth,
+        provider,
+        codex_home,
+        environment_manager,
+        state_db,
+    )
 }
 
 pub async fn start_thread_with_user_shell_override(