Experimental Async Refreshes API (#34918)

app/controllers/api/v1/timelines/home_controller.rb

@@ -1,6 +1,8 @@
 # frozen_string_literal: true
 
 class Api::V1::Timelines::HomeController < Api::V1::Timelines::BaseController
+  include AsyncRefreshesConcern
+
   before_action -> { doorkeeper_authorize! :read, :'read:statuses' }, only: [:show]
   before_action :require_user!, only: [:show]
 
@@ -12,6 +14,8 @@ class Api::V1::Timelines::HomeController < Api::V1::Timelines::BaseController
       @relationships = StatusRelationshipsPresenter.new(@statuses, current_user&.account_id)
     end
 
+    add_async_refresh_header(account_home_feed.async_refresh, retry_seconds: 5)
+
     render json: @statuses,
            each_serializer: REST::StatusSerializer,
            relationships: @relationships,