Is there a vinyl or laminate square that looks like ceramic tile?
Yes several brands. HD carries the Allure brand.
HD offered a groutable vinyl tile that came with a specific grout to be used. I laid two floors using this tile and they look very much like ceramic tile. It was the best discovery I had made in a long while. But....I purchased tile for a third floor without getting the grout at the same time. My big mistake...when I went back for the grout I found they had discontinued it. Not the tile but the grout. This tile and grout was "exclusive" to HD.
They offer an alternative grout but no one there was able to vouch for it. It also only came sanded and I had previously used non-sanded grout. I'm now in the process of trying to find a suitable non-sanded grout to finish my third floor. How can they offer half a product ? They called it a reset.
I personally don't like any textured flooring due to cleaning difficulty. When I bought a new house 5 years ago I got a lino that looked like wood. It looks so much like wood, guests compliment me on the wood flooring. I had tile at my last house, but thankfully only for the bathroom and entry way floor. I hated it.