If I was in the market for a new projector around this budget I wouldn't bother with any of these Faux K, supposedly HDR models. I would go for something like a Sony HW45ES. "Only" 1080p but overall a far superior picture for the money.
There is hardly and 4K steaming content anyway, and UHD's cost a small fortune.
But projectors in general and certainly at this price point can't do HDR, so it is just a meaningless spec to try and sell the product. As for 4K, most streamed HD content looks considerably worse that Blu ray due to compression so I don't see how 4K would be any different.
Projectors are very different beasts from TVs, it's not all about resolution. You could spend 25K on a Sim2 1080p projector. That tells you all you need to know really.
Artifacts, by definition, are things which were not in the original 4K image, so it's not true to say that it's displaying all of the 4K pixels correctly. How much difference that makes in practice is open to debate though.