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-client/src/lib.rs

@@ -29,6 +29,7 @@ pub use codex_app_server::in_process::DEFAULT_IN_PROCESS_CHANNEL_CAPACITY;
 pub use codex_app_server::in_process::InProcessServerEvent;
 use codex_app_server::in_process::InProcessStartArgs;
 use codex_app_server::in_process::LogDbLayer;
+pub use codex_app_server::in_process::StateDbHandle;
 use codex_app_server_protocol::ClientInfo;
 use codex_app_server_protocol::ClientNotification;
 use codex_app_server_protocol::ClientRequest;
@@ -46,7 +47,6 @@ use codex_config::LoaderOverrides;
 use codex_config::NoopThreadConfigLoader;
 use codex_config::RemoteThreadConfigLoader;
 use codex_config::ThreadConfigLoader;
-pub use codex_core::StateDbHandle;
 use codex_core::config::Config;
 pub use codex_exec_server::EnvironmentManager;
 pub use codex_exec_server::EnvironmentManagerArgs;
@@ -951,7 +951,7 @@ mod tests {
     use codex_app_server_protocol::ToolRequestUserInputParams;
     use codex_app_server_protocol::ToolRequestUserInputQuestion;
     use codex_core::config::ConfigBuilder;
-    use codex_core::init_state_db_from_config;
+    use codex_core::init_state_db;
     use futures::SinkExt;
     use futures::StreamExt;
     use pretty_assertions::assert_eq;
@@ -1017,7 +1017,7 @@ mod tests {
     ) -> TestClient {
         let codex_home = TempDir::new().expect("temp dir");
         let config = Arc::new(build_test_config_for_codex_home(codex_home.path()).await);
-        let state_db = init_state_db_from_config(config.as_ref())
+        let state_db = init_state_db(config.as_ref())
             .await
             .expect("state db should initialize for in-process test");
         let client = InProcessAppServerClient::start(InProcessClientStartArgs {