Hibermate are very good, I use them especially when travelling. Original style are reasonably priced https://www.hibermate.com/products/the-original-hibermate

I've been delighted with "Mack's shut-eye shade premium sleep mask" for years. I've only needed to replace my original once.

I started using these when I was a traveling consultant, and now use it only for travel, when taking an afternoon nap, or sleeping in (usually due to illness).

It's very comfortable. The nose bridge is padded. There are two straps, from the top and bottom of the sides, so you don't have a strap routing over the ear. I find it lets in the least amount of light of the masks I've tried precisely because of the comfort features. I don't have to try to arrange the mask in some contorted way to get comfort, so it can sit as intended and block light.

The best I've found isn't sold as a sleep mask, but a "heat massage" mask with beads in it. I never heat it, I only use it as a sleep mask, the beads provide a wonderful, and comfortable, light seal.

I’ve been using the wirecutter’s recommended mask for a while and it has been great. It has that same cupped shape that you describe.

this. there are cheap silk ones as well for people who don't mind the fabric on their eyes.

I think he's talking about literal dollar priced masks or giveaway sleep masks which are usually just a tiny piece of fabric around something more solid, which attaches to you by means of an elastic band; the band however resists falling/slipping by pushing on your eyeballs.

It sounds like your mask is a bit better, and probably more expensive that the parent means. I've gotten such cheap masks as giveaways and the few I tried were indeed unbearable for sleeping as it felt like someone was crushing my face.