Can't add sub tab local tasks to admin/content/my_entity

Question

I have a custom content entity list which has its own tab into admin/content/my_entity. The content of this tab is generated by using EntityListBuilder class. Actually, I created it with the drupal console. Now I am trying to add two more subtabs in this way:

my_module.links.menu.yml

entity.my_entity.collection:
  title: 'My entities'
  route_name: entity.my_entity.collection
  description: 'List of my entities'
  parent: system.admin_content
  weight: 0

my_module.links.task.yml

entity.my_entity.list:
  route_name: entity.my_entity.collection
  base_route: system.admin_content
  title: 'List of my entities'
  weight: 10

entity.my_entity.list_tab_default:
  route_name: entity.my_entity.collection
  parent_id: entity.my_entity.collection
  title: 'Property 1'

entity.my_entity.list_tab_two:
  route_name: entity.my_entity.collection_two
  parent_id: entity.my_entity.collection
  title: 'Property 2'

However, I can't get them to display under the parent's tab. Only parent tab is visible. Also, I tried to add these subtabs with the view and I could not make it displayed either. What I am doing wrong here?