Water cannot itself be wet because you can’t get water on water.

I disagree with this assessment.

Water itself is wet. It's an inherent property.

Water on water changes nothing. It's still wet.

Water is a liquid. Water on something not wet makes it wet - through wet water attachment. It's wet as long as it has water attached.

Something not wet submerged in water consequently must be wet. Although it's not particularly verifyable due to its submerged nature. You touching it means also touching all the water around it. But I don't see how it's wet property would be different from it with only a little water on it.

Thinking of a sponge - it will take in water and be considered wet. This also is the case in water. It won't stay indistinguishable.