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/client/src/test.rs

@@ -85,7 +85,7 @@ impl FakeServer {
                             Connection::in_memory(cx.background_executor().clone());
                         let (connection_id, io, incoming) =
                             peer.add_test_connection(server_conn, cx.background_executor().clone());
-                        cx.background_executor().spawn(io).detach();
+                        cx.background_spawn(io).detach();
                         {
                             let mut state = state.lock();
                             state.connection_id = Some(connection_id);