I have to say I disagree with Todd on floating cork in kitchens. There is a huge difference between floated and tile cork. Floated cork's core is mdf or hdf. If you float cork without post install urethane, it WILL swell at the plank edges and remain ruined with a moderate amount of water. By moderate I mean a 16 oz glass of water spilled overnight. Let's face it there are common kitchen spills between "a few drops transferring dishes to dishwasher" and a "flood". those include a kid spilling a class of water a night, a refrigerator defrost drain overflow of half a gallon and a score of other pint to gallons spills that might not be detected for a few hours. Almost always those would have no affect on vinyl tile or sheet, linoleum, stone, ceramic tile or cork tiles, but would be disastrous for laminates or their structural cousins -- floated cork plank. the liquid will get in the seams between the planks and it will swell the the mdf. That doesn't mean it is out of the question. In a smaller kitchen the costs wont be much ($600-$1,000) and you can float it yourself meaning no installation costs. So a $700 risk isn't that much. It is just that people ought to be aware of the risks -- and the reason why EVERY serious flooring pro recommends cork tile over cork+mdf/hdf lock planks in kitchens.

The back of the tile is likely porous so you need something that will grip tightly without eventually sucking the liquid out of whatever adhesive you're using. Gorilla Glue is pretty good as it fills in the tiny pores-youi slightly wet the back of the tile. I've used Liquid Nails to adhere concrete blocks together and it held for a couple years, eventually giving out. But that was outside in the weather.

It is very rare for moisture to come from 'condensation'. So rare it has a name: Sweating Slab Syndrome (SSS). Traditionally SSS is seen in MASSIVE warehouses (40ft ceilings, raw concrete sitting on gravel, poor circulation, racks and stacks preventing air movement) in locations of HIGH humidity with cool ground temps. A 3" air space sitting underneath 3 layers of 'stuff' isn't going to fit into the category of MASSIVE warehouse. It *can happen...in the same way a cat can learn to play the piano. Intensely rare to the point that you don't think Siamese keyboarder when you hear a swingin' ditty coming from a piano bar! The chances of this being moisture moving UP INTO THE HOUSE from the wet ground = 99.999997%. In fact I would bet my first born on it (he's now 6'3" at 15!). Letting a slab 'dry out' is like letting a bottomless lake empty out of the valley bottom. Slabs sit IN dirt. Dirt is ALWAYS damp. In fact, our planet is an ocean world with islands of sea floor sitting above the surface. Our slabs are really more like dish sponges floating in a swimming pool. In relation to the sponge, the swimming pool is an endless source of water. By the time the swimming pool dries out, your sponge will have deteriorated to the point it will have returned to it's base make-up: sand, gravel and some crumbly white stuff. Don't 'wait' for the slab to dry out. It won't happen. You will THINK it has happened, but it won't have done so. To get a finish over the concrete, you need to have a 'dry' slab (you have to spend all that money sealing it) or it will have adhesion issues. To apply porcelain tile you might have to use an 'exterior grade' install because the slab is too wet/pourous. These damp basements get difficult to deal with. I've seen offices in cold basements. No one uses them because they are too cold. But if you are sure you have a 'steam' pipe somewhere that keeps things toasty warm then go for it. But don't think the slab will 'dry'. It won't. The water will evaporate off SO FAST that you can't see the puddles.

I don't like the idea of LVP because of the environmental impact. I have been hoping that with technology there might be a super water resistant coating for hardwood floors. I have looked at Vermont Natural Coatings Super Whey 3500 which is used in commercial buildings, hotels, & restaurants. Vermont Natural Coating Whey water-based poly coating has been used on many sports/ basketball floors which do get lots of wear but not much water/ liquid spills that sit for at least 8 hours. I would never put wood in a bathroom. I have a semi-open concept home. The kitchen is open to the family/ great room so matching flooring makes the room look bigger and more elegant. The entryway flows into the back great room area so I prefer the main floor being the same flooring. I have seen how the water-based poly coatings on solid hardwood wears quite terribly over the years especially in front of the sinks, stoves, and refrigerators. Every design show makes the main floor all wood now unless it's in Florida where they use tile or LVP. The exception is the mudroom/ primary entrance from the garage being tile IF the main floor is hardwood/ engineered wood flooring. I have been looking at the new waterproof engineered flooring but many reviews show many brands have poor scratch resistance. See: https://www.flooringstores.com/blog/waterproof-hardwood-flooring/