The more I think about it, the more I think it should be NOT a pop-up but the game pausing and pulling up a UI panel with all your available Reactions only. So, if an enemy triggers AOO, the game pauses and the UI only shows Melee attack as an option of what you can do. If you're a rogue who hasn't used Sneak Attack, the Sneak Attack button appears as well, giving you the option to use it.
But maybe you wouldn't want to Sneak Attack because the enemy only has 5 HP. That's why it pops up as an option and it's not automatic.
It would work the same for Battlemaster. AOO triggers. Game pauses. Melee attack and all Battlemaster maneuvers pop up on the UI.
For paladin, same thing except Smite options.
So no message popups. Just game pauses and UI presents your options.