feat: use ProcessId in exec-server (#15866)

Use a full struct for the ProcessId to increase readability and make it
easier in the future to make it evolve if needed

codex-rs/exec-server/tests/process.rs

@@ -6,6 +6,7 @@ use codex_app_server_protocol::JSONRPCMessage;
 use codex_app_server_protocol::JSONRPCResponse;
 use codex_exec_server::ExecResponse;
 use codex_exec_server::InitializeParams;
+use codex_exec_server::ProcessId;
 use common::exec_server::exec_server;
 use pretty_assertions::assert_eq;
 
@@ -62,7 +63,7 @@ async fn exec_server_starts_process_over_websocket() -> anyhow::Result<()> {
     assert_eq!(
         process_start_response,
         ExecResponse {
-            process_id: "proc-1".to_string()
+            process_id: ProcessId::from("proc-1")
         }
     );