Feels like the old CRT days might've had some interesting things you could do.

Unfortunately no, they used RGB just like modern monitors.

The only kind I'm aware of is the Beam Index tube (aka Indextron), which used invisible UV phosphors to synchronize the beam. (Avoiding the need for a shadow mask, making the tube brighter and less sensitive to magnets.)

https://en.wikipedia.org/wiki/Beam-index_tube

https://youtube.com/watch?v=_b7omGhw7wc

But in principle the phosphors used might have some power outside the visual spectrum, making them look different to an eye that can see into the near UV or IR. A lot of UV in particular would be filtered by the thick glass though, I guess.

Tetrachromats from my understanding don't see more of the spectrum, they just have better discrimination of the colors within it.