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How would I go about removing this sink and vanity?
(lemmy.world)
How are these usually attached to the wall? Can I just pry them off or would that damage the drywall?
And follow up questions: how can I reproduce that texture when painting the newly exposed areas of the wall?
No it's likely glued to wall. It can and will rip the drywall. If you get a large thin scraper you can try to push it between the wall and splash guard. (Like a 12" taping knife)
And matching the texture will be very hard. It looks like some type of knockdown or medium orange peel. It's possible the texture is in drywall and was done before vanity installed.