New cabinets and reuse the top - correct? A stone fabricator can remove the top and install it on the new cabs. BUT, the new cabs must be installed first, ask for a referral for that portion of the job.

Or if you want a table rather than a built-in desk, just have the support and legs made by an ironworker or the like.

You can purchase legs from IKEA but a stone guy has to remove the countertop and there is no guarantee it won't break.

https://www.ikea.com/us/en/cat/legs-trestles-11845/

Good question about the tile. We replaced a bathroom cabinet with a pedestal sink. Guess what! No tile under cabinet! What a surprise! Managed to find similar tile, thank goodness.

There are all sorts of table legs available on line; most big box stores also will have wooden ones in stock.

It does not seem that it would be difficult - perhaps even a jack with a sturdy piece of plywood could lift the top enough to get the cabinets out (it is possible that the top isn't actually secured to the cabinets in any way).

Take the bottom drawers all the way out and take a look to see if there is tile underneath.