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/tests/common/test_codex.rs

@@ -15,9 +15,7 @@ use anyhow::anyhow;
 use codex_config::CloudRequirementsLoader;
 use codex_core::CodexThread;
 use codex_core::ThreadManager;
-use codex_core::agent_graph_store_from_state_db;
 use codex_core::config::Config;
-use codex_core::init_state_db_from_config;
 use codex_core::resolve_installation_id;
 use codex_core::shell::Shell;
 use codex_core::shell::get_shell_by_model_provided_path;
@@ -426,33 +424,19 @@ impl TestCodexBuilder {
         environment_manager: Arc<codex_exec_server::EnvironmentManager>,
     ) -> anyhow::Result<TestCodex> {
         let auth = self.auth.clone();
-        let thread_manager = if config.model_catalog.is_some() {
-            let state_db = init_state_db_from_config(&config)
-                .await
-                .expect("test codex 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?;
-            ThreadManager::new(
-                &config,
-                codex_core::test_support::auth_manager_from_auth(auth.clone()),
-                SessionSource::Exec,
-                Arc::clone(&environment_manager),
-                /*analytics_events_client*/ None,
-                state_db,
-                thread_store,
-                agent_graph_store,
-                installation_id,
-            )
-        } else {
-            codex_core::test_support::thread_manager_with_models_provider_and_home(
-                auth.clone(),
-                config.model_provider.clone(),
-                config.codex_home.to_path_buf(),
-                Arc::clone(&environment_manager),
-            )
-            .await
-        };
+        let state_db = codex_core::init_state_db(&config).await;
+        let thread_store = thread_store_from_config(&config, state_db.clone());
+        let installation_id = resolve_installation_id(&config.codex_home).await?;
+        let thread_manager = ThreadManager::new(
+            &config,
+            codex_core::test_support::auth_manager_from_auth(auth.clone()),
+            SessionSource::Exec,
+            Arc::clone(&environment_manager),
+            /*analytics_events_client*/ None,
+            thread_store,
+            state_db.clone(),
+            installation_id,
+        );
         let thread_manager = Arc::new(thread_manager);
         let user_shell_override = self.user_shell_override.clone();