Should wearing armor cause issues when sleeping?

I’m not sure. I think that if you would be wearing it, instead of it covering you, it might still be a problem.

It depends a lot on the material though. 20kg of steel armor or 20 kg of fur and wool would make a big difference.

Hmm material based encumberance comfort? Rather than item based?

It would catch some items, but not all.
For example, there’s plenty of cloth and wool things which have embroidery, buttons, have an odd shapes or otherwise stuff that would dig into your skin if you sleep with them on, there’s things that can chafe with the usual friction of sleeping, but things of the same material that have a softer lining to prevent said chafing.

On more concrete examples after checking about half of armor.json:
A bowler hat or a 10-galon hat would be uncomfortable to sleep in unless you assume the player takes it off and just places it on top of their face, but a beanie or a ski mask might not need to do that. The nomad armor might be designed to be comfortable to be worn for long periods of time, or even sleep in it despite listing leather as one of it’s materials.

Backpacks and other stuff in the STRAPPED or WAIST layers could be uncomfortable to sleep with regardless of material (and duffel bags are cotton), but you could assume that the player takes it off before laying down. Ditto for bindles.

A badge is made out of metal, but would only be uncomfortable in some positions. There’s plenty of people that can sleep with their watches, rings, bracelets and so on worn without discomfort regardless of them being made out of plastic and metals.

A beekeeping suit is probably uncomfortable to sleep in even without the hood, despite being made out of cotton (wouldn’t know, I’ve never worn one)

Blazers, lab coats, dress shirts and wedding dresses would likely be uncomfortable, either due to buttons or some other aspect like the cut or the embroidery, despite being “cotton”.

Some of the leather underclothes might be comfortable to sleep in, but leather armor would not be.