The case doesn't go over any part of the visible area of the screen, and with a tempered screen protector it's only slightly raised. It's definitely not a chunky case.
Regarding scratching from a case, I've had that in the past. Due to my job I can end up with dust and grit in the pockets of my work trousers which would somehow find its way in between the phone and the case and mark it around the edges. To avoid this I put a skin on my phone. Since I've started doing this my phones have always been immaculate when I remove the case and skin a year or 2 later when i upgrade and sell it on. They aren't expensive, just a little fiddly to put on but worth it if you're concerned of scratching/marking it.
For example:
https://www.xtremeskins.co.uk/products/google-pixel-5-skins?variant=33090901737535