Should you include a branded QR code?
Yes, if the code opens the menu or the booking message and it scans from where it sits. Do not put it as ornament inside the mark if it stops being readable when reduced.
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Test the link on a phone, standing, at the distance of the poster. The QR sits inside the drawing and the camera cannot catch it. You get the code apart from the mark, at a size that has been scanned, on the current link.