Note: this ticket was not completed during the sprint. The follow up ticket T405746: Codex: Teleport Menus by default (part 2) resolves the remaining pieces.
Just like Dialogs, Menus should automatically teleport if a TeleportTarget is provided. This would avoid menus getting cut off by things like sticky headers, as seen at T379836#10823078. It would also help with (but not entirely fix) T379947.
For Menus inside Dialogs, teleportation alone doesn't guarantee that the Menu will appear on top of the Dialog if both are teleported. For this case we will probably have to have each Dialog create its own teleport target and provide that to the components inside it.
The Reader Experience team will provide code review.