feat(ui): Use the new latest_event sorter in the room list.

This patch installs the `new_sorter_latest_event` in the room list.

crates/matrix-sdk-base/src/room/room_info.rs

@@ -1050,7 +1050,7 @@ impl RoomInfo {
 
     /// Updates the recency stamp of this room.
     ///
-    /// Please read [`Self::recency_stamp`] to learn more.
+    /// Please read `Self::recency_stamp` to learn more.
     pub fn update_recency_stamp(&mut self, stamp: u64) {
         self.recency_stamp = Some(stamp);
     }

crates/matrix-sdk-ui/src/room_list_service/room_list.rs

@@ -37,6 +37,7 @@ use super::{
     filters::BoxedFilterFn,
     sorters::{new_sorter_lexicographic, new_sorter_name, new_sorter_recency},
 };
+use crate::room_list_service::sorters::new_sorter_latest_event;
 
 /// A `RoomList` represents a list of rooms, from a
 /// [`RoomListService`](super::RoomListService).
@@ -165,7 +166,16 @@ impl RoomList {
                 let (values, stream) = (raw_values, merged_streams)
                     .filter(filter_fn)
                     .sort_by(new_sorter_lexicographic(vec![
+                        // Sort by latest event's kind, i.e. put the rooms with a
+                        // **local** latest event first.
+                        Box::new(new_sorter_latest_event()),
+
+                        // Sort rooms by their recency (either by looking
+                        // at their latest event's timestamp, or their
+                        // `recency_stamp`).
                         Box::new(new_sorter_recency()),
+
+                        // Finally, sort by name.
                         Box::new(new_sorter_name())
                     ]))
                     .dynamic_head_with_initial_value(page_size, limit_stream.clone());