fix: send unfiltered models over model/list (#11793)

### What
to unblock filtering models in VSCE, change `model/list` app-server
endpoint to send all models + visibility field `showInPicker` so
filtering can be done in VSCE if desired.

### Tests
Updated tests.

codex-rs/app-server/tests/suite/v2/model_list.rs

@@ -33,6 +33,7 @@ async fn list_models_returns_all_models_with_large_limit() -> Result<()> {
         .send_list_models_request(ModelListParams {
             limit: Some(100),
             cursor: None,
+            include_hidden: None,
         })
         .await?;
 
@@ -54,6 +55,7 @@ async fn list_models_returns_all_models_with_large_limit() -> Result<()> {
             upgrade: None,
             display_name: "gpt-5.2-codex".to_string(),
             description: "Latest frontier agentic coding model.".to_string(),
+            hidden: false,
             supported_reasoning_efforts: vec![
                 ReasoningEffortOption {
                     reasoning_effort: ReasoningEffort::Low,
@@ -84,6 +86,7 @@ async fn list_models_returns_all_models_with_large_limit() -> Result<()> {
             upgrade: Some("gpt-5.2-codex".to_string()),
             display_name: "gpt-5.1-codex-max".to_string(),
             description: "Codex-optimized flagship for deep and fast reasoning.".to_string(),
+            hidden: false,
             supported_reasoning_efforts: vec![
                 ReasoningEffortOption {
                     reasoning_effort: ReasoningEffort::Low,
@@ -114,6 +117,7 @@ async fn list_models_returns_all_models_with_large_limit() -> Result<()> {
             upgrade: Some("gpt-5.2-codex".to_string()),
             display_name: "gpt-5.1-codex-mini".to_string(),
             description: "Optimized for codex. Cheaper, faster, but less capable.".to_string(),
+            hidden: false,
             supported_reasoning_efforts: vec![
                 ReasoningEffortOption {
                     reasoning_effort: ReasoningEffort::Medium,
@@ -138,6 +142,7 @@ async fn list_models_returns_all_models_with_large_limit() -> Result<()> {
             description:
                 "Latest frontier model with improvements across knowledge, reasoning and coding"
                     .to_string(),
+            hidden: false,
             supported_reasoning_efforts: vec![
                 ReasoningEffortOption {
                     reasoning_effort: ReasoningEffort::Low,
@@ -173,6 +178,38 @@ async fn list_models_returns_all_models_with_large_limit() -> Result<()> {
     Ok(())
 }
 
+#[tokio::test]
+async fn list_models_includes_hidden_models() -> Result<()> {
+    let codex_home = TempDir::new()?;
+    write_models_cache(codex_home.path())?;
+    let mut mcp = McpProcess::new(codex_home.path()).await?;
+
+    timeout(DEFAULT_TIMEOUT, mcp.initialize()).await??;
+
+    let request_id = mcp
+        .send_list_models_request(ModelListParams {
+            limit: Some(100),
+            cursor: None,
+            include_hidden: Some(true),
+        })
+        .await?;
+
+    let response: JSONRPCResponse = timeout(
+        DEFAULT_TIMEOUT,
+        mcp.read_stream_until_response_message(RequestId::Integer(request_id)),
+    )
+    .await??;
+
+    let ModelListResponse {
+        data: items,
+        next_cursor,
+    } = to_response::<ModelListResponse>(response)?;
+
+    assert!(items.iter().any(|item| item.hidden));
+    assert!(next_cursor.is_none());
+    Ok(())
+}
+
 #[tokio::test]
 async fn list_models_pagination_works() -> Result<()> {
     let codex_home = TempDir::new()?;
@@ -185,6 +222,7 @@ async fn list_models_pagination_works() -> Result<()> {
         .send_list_models_request(ModelListParams {
             limit: Some(1),
             cursor: None,
+            include_hidden: None,
         })
         .await?;
 
@@ -207,6 +245,7 @@ async fn list_models_pagination_works() -> Result<()> {
         .send_list_models_request(ModelListParams {
             limit: Some(1),
             cursor: Some(next_cursor.clone()),
+            include_hidden: None,
         })
         .await?;
 
@@ -229,6 +268,7 @@ async fn list_models_pagination_works() -> Result<()> {
         .send_list_models_request(ModelListParams {
             limit: Some(1),
             cursor: Some(third_cursor.clone()),
+            include_hidden: None,
         })
         .await?;
 
@@ -251,6 +291,7 @@ async fn list_models_pagination_works() -> Result<()> {
         .send_list_models_request(ModelListParams {
             limit: Some(1),
             cursor: Some(fourth_cursor.clone()),
+            include_hidden: None,
         })
         .await?;
 
@@ -283,6 +324,7 @@ async fn list_models_rejects_invalid_cursor() -> Result<()> {
         .send_list_models_request(ModelListParams {
             limit: None,
             cursor: Some("invalid".to_string()),
+            include_hidden: None,
         })
         .await?;