Im wondering what kind of tv to look for?
IMO 4k is useless because the network where I live is bad and 1080p is good enough. I don’t think smart tv functionality is a thing to look for, more like a « what not to look for » criteria.
What other criterions should be taken?
They are called computer monitors. There are also commercial sign displays, but the picture quality is usually not very good.
IIYAMA make DSDs that are 4K, although I know that’s not a requirement for OP, so that should be able to replace a TV pretty well