How do I do this for multiple buttons? When I try the same events with another button, it only appears for one frame?
The trigger once will only work well with just one object.
You will need to use instead a variable to make it work for each object individually.
The questions here to solve are:
1-If you have multiple objects and you stop overlapping just one of them what happens? are you destroying all the buttons? because you are still overlapping the other one.
2-If each "NewGameButton" spawns a "ButtonSelect" and has to be linked to that specific button so only he can destroy it, then you will need something to link them like a variable or Hierarchy so when you need to destroy it you can easily pick the right one.
If you give a bit more info of what is your goal it will be easier to give you the correct answer.