You should be able to sit on the sofa (or even the chair) in the Apartment to recover your sleep. Though this recovery is slow and Sleep consumables are encouraged!
I should probably make the Hunger and Sleep slower I guess
And the screen should not remain grey when you die, I tested it several times and it was working fine, hopefully it's a rare bug
There's also a Hypersleep Chamber which can be unlocked as you upgrade your Apartment
