Don't stress, that's by far the hardest puzzle, and it's bonus content, not required for the basic endings.
Hint: The buttons are arranged in columns, and you need to push the right one in each column. The key for which button is in plain sight around the room.
Spoiler: If you'd like the answer, check out the ending guide post here: https://desidee.itch.io/changing-time-vr/devlog/754383/ending-list