For what it's worth, I always knock a star or two off my review for a restaurant if they won't give me a paper menu. It's fine if they lead with the qr code but I want to at least be able to ask for a physical one.
Make sure they are popups too that occur randomly as they scroll through the menu to increase their engagement.
Also ensure you add in some hidden dark patterns like ticking default for donating to some sketchy charity during the payment process.
In general I don't think I'd find a digital menu with ads all that much more objectionable than one without, I'm pretty desensitized to digital ads at this point.