Should the tightness of the QR skewer (rear wheel) affect the freewheel

You just noticed that quick release tightness affects the bearing preload.

If your hub has cup and cone bearings, you can adjust the bearing preload so that you are able to tighten the QR skewer to maximum tightness without the bearings being too tight. This is one of the advantages of cup and cone bearings and part of the reason why cup and cone bearings are preferable for hubs. Use cone spanners to adjust the bearings. You can measure the required cone spanner size with vernier calipers. Instructions for adjusting the hub bearings.

If your hub has cartridge bearings, there's little you can do. The tightness of these bearings cannot be adjusted.

You should normally be able to install the quick release with adequate force to hold the wheel, with a freely spinning hub. Tightening the quick release does have a small effect on the hubs but yours is seemingly exaggerated, and you have a noticeable creaky noise which presumably you didn't have before. I think you therefore have an issue inside the hub to do with the wheel bearings, creaks are a sign of something that needs your attention but can be put right.

In other words your hub needs a service of some description.

I don't think it's normal, I think you should be able to tighten the QR much harder than necessary without impeding the wheel rotation.

I'm only familiar with slightly older Giant wheels, but I believe one of the distinctions between the S-R2 and the P-R2 wheelsets was cup and cone vs cartridge bearings respectively.

Either way, a hub service is the way to go. If you have cup and cone bearings it may be that they need inspection and cleaning only, or something could be worn out in there. Maybe the locknuts just are loose and not holding the preload like they should. If you have cartridge bearings and something has worn out badly, they can be replaced. My older P-R2 has a shouldered axle, so when I remove the axle end caps, the axle remains in place and so do the bearings. then if there was any play when I wiggle the end of the axle it would show wear of the cartridge.

The first inspection you can make is to remove the wheel from the bike and the QR, then wiggle the axle and see if there's any play, there should be none. The nuts on the threaded axle should be tightly secured as well, if you can spin any threaded nut by hand then something has come loose.

Hopefully no fragments of metal have damaged the slightly more expensive hub internals but the only way to find out is getting in there to have a look and sooner rather than later.