Make fallback user mentions support also match against the bot's room-specific username

It seems like Element iOS benefits from this.

src/bot/implementation.rs

@@ -172,6 +172,24 @@ impl Bot {
         self.matrix_link().user_id()
     }
 
+    pub(crate) async fn user_display_name_in_room(&self, room: &Room) -> Option<String> {
+        let bot_display_name = self
+            .room_display_name_fetcher()
+            .own_display_name_in_room(room)
+            .await;
+
+        match bot_display_name {
+            Ok(value) => value,
+            Err(err) => {
+                tracing::warn!(
+                    ?err,
+                    "Failed to fetch bot display name. Proceeding without it"
+                );
+                None
+            }
+        }
+    }
+
     pub(crate) fn reacting(&self) -> super::reacting::Reacting {
         super::reacting::Reacting::new(self.clone())
     }

src/bot/messaging.rs

@@ -239,8 +239,11 @@ impl Messaging {
             }
         };
 
+        let bot_display_name = self.bot.user_display_name_in_room(&room).await;
+
         let interaction_context = determine_interaction_context_for_room_event(
             self.bot.user_id(),
+            &bot_display_name,
             &room,
             &event,
             &payload,
@@ -279,7 +282,8 @@ impl Messaging {
             self.bot.admin_pattern_regexes().clone(),
             trigger_event_info,
             interaction_context.thread_info.clone(),
-        );
+        )
+        .with_bot_display_name(bot_display_name);
 
         let controller_type = crate::controller::determine_controller(
             self.bot.command_prefix(),