cx.background_executor().spawn(...) -> cx.background_spawn(...) (#25103)

Done automatically with

> ast-grep -p '$A.background_executor().spawn($B)' -r
'$A.background_spawn($B)' --update-all --globs "\!crates/gpui"

Followed by:

* `cargo fmt`
* Unexpected need to remove some trailing whitespace.
* Manually adding imports of `gpui::{AppContext as _}` which provides
`background_spawn`
* Added `AppContext as _` to existing use of `AppContext`

Release Notes:

- N/A

crates/assistant2/src/context_picker/thread_context_picker.rs

@@ -123,7 +123,7 @@ impl PickerDelegate for ThreadContextPickerDelegate {
         };
 
         let executor = cx.background_executor().clone();
-        let search_task = cx.background_executor().spawn(async move {
+        let search_task = cx.background_spawn(async move {
             if query.is_empty() {
                 threads
             } else {