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/project/src/debugger/session.rs

@@ -191,8 +191,8 @@ impl LocalMode {
         messages_tx: futures::channel::mpsc::UnboundedSender<Message>,
         cx: AsyncApp,
     ) -> Task<Result<(Self, Capabilities)>> {
-        cx.spawn(move |mut cx| async move {
-            let (adapter, binary) = Self::get_adapter_binary(&config, &delegate, &mut cx).await?;
+        cx.spawn(async move |cx| {
+            let (adapter, binary) = Self::get_adapter_binary(&config, &delegate,  cx).await?;
 
             let message_handler = Box::new(move |message| {
                 messages_tx.unbounded_send(message).ok();
@@ -439,7 +439,7 @@ impl LocalMode {
 
         let configuration_sequence = cx.spawn({
             let this = self.clone();
-            move |cx| async move {
+            async move |cx| {
                 initialized_rx.await?;
                 // todo(debugger) figure out if we want to handle a breakpoint response error
                 // This will probably consist of letting a user know that breakpoints failed to be set
@@ -697,7 +697,7 @@ impl Session {
     ) -> Task<Result<Entity<Self>>> {
         let (message_tx, mut message_rx) = futures::channel::mpsc::unbounded();
 
-        cx.spawn(move |mut cx| async move {
+        cx.spawn(async move |cx| {
             let (mode, capabilities) = LocalMode::new(
                 session_id,
                 parent_session.clone(),
@@ -710,31 +710,30 @@ impl Session {
             .await?;
 
             cx.new(|cx| {
-                let _background_tasks =
-                    vec![cx.spawn(move |this: WeakEntity<Self>, mut cx| async move {
-                        let mut initialized_tx = Some(initialized_tx);
-                        while let Some(message) = message_rx.next().await {
-                            if let Message::Event(event) = message {
-                                if let Events::Initialized(_) = *event {
-                                    if let Some(tx) = initialized_tx.take() {
-                                        tx.send(()).ok();
-                                    }
-                                } else {
-                                    let Ok(_) = this.update(&mut cx, |session, cx| {
-                                        session.handle_dap_event(event, cx);
-                                    }) else {
-                                        break;
-                                    };
+                let _background_tasks = vec![cx.spawn(async move |this: WeakEntity<Self>, cx| {
+                    let mut initialized_tx = Some(initialized_tx);
+                    while let Some(message) = message_rx.next().await {
+                        if let Message::Event(event) = message {
+                            if let Events::Initialized(_) = *event {
+                                if let Some(tx) = initialized_tx.take() {
+                                    tx.send(()).ok();
                                 }
                             } else {
-                                let Ok(_) = start_debugging_requests_tx
-                                    .unbounded_send((session_id, message))
-                                else {
+                                let Ok(_) = this.update(cx, |session, cx| {
+                                    session.handle_dap_event(event, cx);
+                                }) else {
                                     break;
                                 };
                             }
+                        } else {
+                            let Ok(_) =
+                                start_debugging_requests_tx.unbounded_send((session_id, message))
+                            else {
+                                break;
+                            };
                         }
-                    })];
+                    }
+                })];
 
                 cx.subscribe(&breakpoint_store, |this, _, event, cx| match event {
                     BreakpointStoreEvent::BreakpointsUpdated(path, reason) => {
@@ -1102,17 +1101,17 @@ impl Session {
             let error = Err(anyhow::Error::msg(
                 "Couldn't complete request because it's not supported",
             ));
-            return cx.spawn(|this, mut cx| async move {
-                this.update(&mut cx, |this, cx| process_result(this, error, cx))
+            return cx.spawn(async move |this, cx| {
+                this.update(cx, |this, cx| process_result(this, error, cx))
                     .log_err()
                     .flatten()
             });
         }
 
         let request = mode.request_dap(session_id, request, cx);
-        cx.spawn(|this, mut cx| async move {
+        cx.spawn(async move |this, cx| {
             let result = request.await;
-            this.update(&mut cx, |this, cx| process_result(this, result, cx))
+            this.update(cx, |this, cx| process_result(this, result, cx))
                 .log_err()
                 .flatten()
         })