Hi Jane, thanks for reading, I appreciate it!
You're exactly right that the K371, and indeed most closed-back headphones, rely on a proper seal in order to deliver their sound signature correctly into your ears.
I test every single headphone I review wearing my glasses, and so you can take my impressions of each headphone as such. Unfortunately, I can only really test stuff out with my specific glasses and my specific head shape, haha. I do have thin glasses that sit pretty close to my head. If I have any issues with the glasses and seal, I mention them in the review.
With my specific glasses, I'll sometimes get a small break in the seal that results in a bit less sub-bass response. I compare bass-heavy test tracks with and without my glasses to see how dramatic this effect is and it's almost always minor enough in my particular case to not be worth mentioning.
You shouldn't hear any squeaky noises from the pads against your glasses unless you're moving your face a great deal while listening, but again, I can only speak to my personal experiences with my personal glasses.
Rtings.com tries to simulate seal issues in their frequency response consistency measurements and that might be a good resource for you to find closed-back pairs that don't have major issues with glasses. You could also consider open backed headphones. They're usually designed in such a way as to not need a significant seal, and aren't usually impacted much by glasses in my experience.