Is it normal to instruct an aircraft to squawk VFR if it goes around on an IFR visual approach?
No, that scenario does not sound normal to me. For one thing, a visual approach is an IFR procedure. Instructing the crew to change to a VFR squawk makes it sound like the controller is suddenly treating the flight as a VFR flight, which makes no sense. A controller is never allowed to just cancel IFR; going from IFR to VFR must always be explicitly requested by the crew ("cancelling my IFR flight"). We are not even allowed to suggest a flight to change to VFR, the idea has to come from the pilot.

Besides, it makes no sense that the controller would change the squawk code of a (presumably) already identified flight to a non-discreet code (1200/7000) since radar identification would then be lost and it would be impossibly to continue to provide radar service.

If the example you provide is a real one, there is obviously a reason for the controller doing what they did, however, based on the limited information you give here, it is hard to see what the reason would be. Maybe if we knew the whole picture, it would make more sense.