Move "async move" a few characters to the left in cx.spawn() (#26758)

This is the core change:
https://github.com/zed-industries/zed/pull/26758/files#diff-044302c0d57147af17e68a0009fee3e8dcdfb4f32c27a915e70cfa80e987f765R1052

TODO:
- [x] Use AsyncFn instead of Fn() -> Future in GPUI spawn methods
- [x] Implement it in the whole app
- [x] Implement it in the debugger 
- [x] Glance at the RPC crate, and see if those box future methods can
be switched over. Answer: It can't directly, as you can't make an
AsyncFn* into a trait object. There's ways around that, but they're all
more complex than just keeping the code as is.
- [ ] Fix platform specific code

Release Notes:

- N/A

crates/context_server/src/client.rs

@@ -171,13 +171,17 @@ impl Client {
             let notification_handlers = notification_handlers.clone();
             let response_handlers = response_handlers.clone();
             let transport = transport.clone();
-            move |cx| {
+            async move |cx| {
                 Self::handle_input(transport, notification_handlers, response_handlers, cx)
                     .log_err()
+                    .await
             }
         });
-        let stderr_input_task = cx.spawn(|_| Self::handle_stderr(transport.clone()).log_err());
-        let input_task = cx.spawn(|_| async move {
+        let stderr_input_task = cx.spawn({
+            let transport = transport.clone();
+            async move |_| Self::handle_stderr(transport).log_err().await
+        });
+        let input_task = cx.spawn(async move |_| {
             let (stdout, stderr) = futures::join!(stdout_input_task, stderr_input_task);
             stdout.or(stderr)
         });
@@ -217,7 +221,7 @@ impl Client {
         transport: Arc<dyn Transport>,
         notification_handlers: Arc<Mutex<HashMap<&'static str, NotificationHandler>>>,
         response_handlers: Arc<Mutex<Option<HashMap<RequestId, ResponseHandler>>>>,
-        cx: AsyncApp,
+        cx: &mut AsyncApp,
     ) -> anyhow::Result<()> {
         let mut receiver = transport.receive();