code-mode: Remove Session::is_alive() (#29732)

Remove this unused API. This API is insidious in that it implies that
alive state should be determinable from the caller, and implies that a
preflight should indicate routing. Lets drop this, and handle errors
correctly from a failed session in the future.

codex-rs/code-mode/src/service.rs

@@ -216,10 +216,6 @@ impl Default for InProcessCodeModeSession {
 }
 
 impl CodeModeSession for InProcessCodeModeSession {
-    fn is_alive(&self) -> bool {
-        self.runtime.is_alive()
-    }
-
     fn execute<'a>(
         &'a self,
         request: ExecuteRequest,