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/prompt_debug.rs

@@ -17,9 +17,8 @@ use crate::resolve_installation_id;
 use crate::session::session::Session;
 use crate::session::turn::build_prompt;
 use crate::session::turn::built_tools;
+use crate::state_db_bridge::StateDbHandle;
 use crate::thread_manager::ThreadManager;
-use crate::thread_manager::agent_graph_store_from_state_db;
-use crate::thread_manager::init_state_db_from_config;
 use crate::thread_manager::thread_store_from_config;
 
 /// Build the model-visible `input` list for a single debug turn.
@@ -27,6 +26,7 @@ use crate::thread_manager::thread_store_from_config;
 pub async fn build_prompt_input(
     mut config: Config,
     input: Vec<UserInput>,
+    state_db: Option<StateDbHandle>,
 ) -> CodexResult<Vec<ResponseItem>> {
     config.ephemeral = true;
 
@@ -38,11 +38,7 @@ pub async fn build_prompt_input(
         config.codex_linux_sandbox_exe.clone(),
     )?;
 
-    let state_db = init_state_db_from_config(&config)
-        .await
-        .ok_or_else(|| std::io::Error::other("prompt debug requires state db"))?;
     let thread_store = thread_store_from_config(&config, state_db.clone());
-    let agent_graph_store = agent_graph_store_from_state_db(state_db.clone());
     let installation_id = resolve_installation_id(&config.codex_home).await?;
     let thread_manager = ThreadManager::new(
         &config,
@@ -50,9 +46,8 @@ pub async fn build_prompt_input(
         SessionSource::Exec,
         Arc::new(EnvironmentManager::new(EnvironmentManagerArgs::new(local_runtime_paths)).await),
         /*analytics_events_client*/ None,
-        state_db,
         thread_store,
-        agent_graph_store,
+        state_db.clone(),
         installation_id,
     );
     let thread = thread_manager.start_thread(config).await?;