Outdoor Pond With Goldfish & Koi

I have an outdoor water feature in Montana with roughly 100 thriving single-tailed common goldfish thriving. I purchased them in 2020 and all but a handful have survived five years. The water feature is 20 feet long, 8 feet wide, 3 feet deep. It contains cold hardy water lily plants and other surface plants I add seasonally. The water recycles using a pump and trickles down a waterfall to aerate, and it is fed with fresh spring water as it evaporates, so it's very clean. There are plentiful rocks along the sides for the fish to hide. In the winter, I use a floating pond heater to keep a hole in the ice.

My daughter is asking if I would add koi fish. I have a few questions:

1. I've read that a minimum of three koi fish are recommended for their mental health. Is this necessary if they're kept with 100 common goldfish, or only if they're the only fish in the pond?

2. Is there any particular type or size of koi fish recommended to best fit the environment described above? I see many for sale on Amazon and also my local Petsmart but am looking for some guidance on what to go with.

Any other tips would be appreciated, too. Thanks!