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.