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/tests/suite/v2/remote_thread_store.rs

@@ -42,7 +42,6 @@ use codex_core::config::ConfigBuilder;
 use codex_exec_server::EnvironmentManager;
 use codex_feedback::CodexFeedback;
 use codex_protocol::protocol::SessionSource;
-use codex_state::StateRuntime;
 use codex_thread_store::InMemoryThreadStore;
 use pretty_assertions::assert_eq;
 use tempfile::TempDir;
@@ -68,13 +67,6 @@ async fn thread_start_with_non_local_thread_store_does_not_create_local_persiste
         .loader_overrides(loader_overrides.clone())
         .build()
         .await?;
-    let sqlite_home = TempDir::new()?;
-    let state_db = StateRuntime::init(
-        sqlite_home.path().to_path_buf(),
-        config.model_provider_id.clone(),
-    )
-    .await
-    .expect("remote thread store regression test should initialize state db");
 
     let thread_store = InMemoryThreadStore::for_id(store_id.clone());
     let _in_memory_store = InMemoryThreadStoreId { store_id };
@@ -88,7 +80,7 @@ async fn thread_start_with_non_local_thread_store_does_not_create_local_persiste
         thread_config_loader: Arc::new(NoopThreadConfigLoader),
         feedback: CodexFeedback::new(),
         log_db: None,
-        state_db: Some(state_db),
+        state_db: None,
         environment_manager: Arc::new(EnvironmentManager::default_for_tests()),
         config_warnings: Vec::new(),
         session_source: SessionSource::Cli,