Remove all the contents and drawers from the vanity.
Turn off/disconnect the plumbing.
Look inside for any screws that would go into the walls and remove those. Specifically around the top, base, and sides of the vanity. You might find how the sink top is attached to the base as well, splitting those will make it lighter but maybe not easier. 100% depends on the assembly.
Cut the caulk between the wall and vanity top. Probably goes all the way around and maybe under the lip.
Lift up on the corner of the top/vanity. Everything should lift up and start breaking away from the wall. It should lift with some weight but you shouldn't have to really leverage on it to move it. If it still feels attached, look for more screws.
To add to step 4: after you cut the caulk try and slide a putty knife between the counter top and the wall to check for adhesive on the backside. If there is adhesive you can try and cut through it with the putty knife that way you don’t rip/peel the drywall as you’re pulling the counter out. The less damage to the dry wall the better.
As for the texturing it is called knock down texturing. It’s done with dry wall compound. Here is a YouTube video showing the patching steps video
Check YouTube for videos of vanity removal they will walk through all the steps above as well.
To add to step 4: after you cut the caulk try and slide a putty knife between the counter top and the wall to check for adhesive on the backside. If there is adhesive you can try and cut through it with the putty knife that way you don’t rip/peel the drywall as you’re pulling the counter out. The less damage to the dry wall the better.
As for the texturing it is called knock down texturing. It’s done with dry wall compound. Here is a YouTube video showing the patching steps video
Check YouTube for videos of vanity removal they will walk through all the steps above as well.
Thank you, that was my main concern.