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.
May have been glued to the wall as well. I would expect to have to repair the drywall. For the texture, they have spray on texture in a can that they say replicates the existing look. I would not expect to get it perfect. It will probably look different no matter how hard you try.
Thank you for the detailed response. So for that raised lip I should expect nothing but caulking on the edges holding it to the wall?
May have been glued to the wall as well. I would expect to have to repair the drywall. For the texture, they have spray on texture in a can that they say replicates the existing look. I would not expect to get it perfect. It will probably look different no matter how hard you try.