"8k" name in this case is just a marketing. It's not 8k, it's 4230p only.
They moved to measuring the long side AND exaggerating by rounding up in the same generation, stealing the name of a slightly-better existing standard in the process.
You're right that 8k makes sense so long as you accept 4k, though.
"4k" means ~2000x4000 pixels and "8k" means ~4000x8000 pixels.
It is 8k and reasonably priced at $1000 new / $752.99 used
It's close enough for the marketing department, and now that's what it's understood to mean.
Now 4K refers to image roughly the width of 4000 pixels according to wikipedia [1]