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/auto_update/src/auto_update.rs

@@ -513,7 +513,7 @@ impl AutoUpdater {
         should_show: bool,
         cx: &App,
     ) -> Task<Result<()>> {
-        cx.background_executor().spawn(async move {
+        cx.background_spawn(async move {
             if should_show {
                 KEY_VALUE_STORE
                     .write_kvp(
@@ -531,7 +531,7 @@ impl AutoUpdater {
     }
 
     pub fn should_show_update_notification(&self, cx: &App) -> Task<Result<bool>> {
-        cx.background_executor().spawn(async move {
+        cx.background_spawn(async move {
             Ok(KEY_VALUE_STORE
                 .read_kvp(SHOULD_SHOW_UPDATE_NOTIFICATION_KEY)?
                 .is_some())