stone veneer on drywall

Depends on the stone to be honest but I am not a big fan of adhesion to drywall. I would wire lathe it at a minimum.

You cannot adhere an adhered veneer to drywall, painted or not. You have 3 choices:

Screw 1/4" hardie backer to the drywall, hitting the studs.

Remove the drywall and screw 1/2" hardi backer to the studs.

Lath over the drywall (or bare studs) and lay down a scratch coat of stucco.

No matter which one you choose, use a polymer modified thinset to attach the veneer.

In some cases, you can adhere thin brick to drywall, but never over painted sheetrock. For thin brick on drywall, a specialized base-coat material is applied and then the brick faces are thinset to it. Suitable for small areas like backsplashes, but not for a fireplace or wall.