Honor null thread instructions (#16964)

- Treat explicit null thread instructions as a blank-slate override
while preserving omitted-field fallback behavior.
- Preserve null through rollout resume/fork and keep explicit empty
strings distinct.
- Add app-server v2 start/fork coverage for the tri-state instruction
params.

codex-rs/codex-api/tests/clients.rs

@@ -266,7 +266,7 @@ async fn streaming_client_retries_on_transport_error() -> Result<()> {
 
     let request = ResponsesApiRequest {
         model: "gpt-test".into(),
-        instructions: "Say hi".into(),
+        instructions: Some("Say hi".into()),
         input: Vec::new(),
         tools: Vec::new(),
         tool_choice: "auto".into(),
@@ -302,7 +302,7 @@ async fn azure_default_store_attaches_ids_and_headers() -> Result<()> {
 
     let request = ResponsesApiRequest {
         model: "gpt-test".into(),
-        instructions: "Say hi".into(),
+        instructions: Some("Say hi".into()),
         input: vec![ResponseItem::Message {
             id: Some("msg_1".into()),
             role: "user".into(),