workspace: Make Item::clone_on_split async (#41211)

Split out from https://github.com/zed-industries/zed/pull/40774 to
reduce the size of the reland of that PR (once I figure out the cause of
the issue)

Release Notes:

- N/A *or* Added/Fixed/Improved ...

crates/workspace/src/pane.rs

@@ -3292,11 +3292,18 @@ impl Pane {
                         else {
                             return;
                         };
-                        if let Some(item) = item.clone_on_split(database_id, window, cx) {
-                            to_pane.update(cx, |pane, cx| {
-                                pane.add_item(item, true, true, None, window, cx);
-                            })
-                        }
+                        let task = item.clone_on_split(database_id, window, cx);
+                        let to_pane = to_pane.downgrade();
+                        cx.spawn_in(window, async move |_, cx| {
+                            if let Some(item) = task.await {
+                                to_pane
+                                    .update_in(cx, |pane, window, cx| {
+                                        pane.add_item(item, true, true, None, window, cx)
+                                    })
+                                    .ok();
+                            }
+                        })
+                        .detach();
                     } else {
                         move_item(&from_pane, &to_pane, item_id, ix, true, window, cx);
                     }