Turning their back to you: they feel safe and trust you.
Putting their butt in your face: they want you to lick it, as their mother would.
Obviously, don’t do that, but instead, give their haunches and above-the-tail backside a good scritch
Rolling on their back: they’re exposing their vulnerable stomachs to you as a show of trust. this is not an invitation to touch their stomach
slowly closing their eyes while looking at you: this is also a sign of trust. You can do it back to them to make them happier
Putting their butt in your face: they want you to lick it, as their mother would. Obviously, don’t do that, but instead, give their haunches and above-the-tail backside a good scritch
Unless the cat is in the same position pictured in op, because in my experience their tail will go up and you will have a butthole directly in your face 😂
https://vetexplainspets.com/why-do-cats-lick-other-cats-butts/
One of the main reasons cats lick each other’s butts is for grooming purposes. Cats are meticulous groomers and spend a significant amount of time cleaning themselves and their fellow feline companions. Licking each other’s butts allows cats to clean hard-to-reach areas and helps maintain their hygiene.
The cat looked unhappily back at its butt. The problems resulting from concurrently wearing a built-in fur coat, pooping, and not having any hands to operate toilet paper were clearly not appreciated by the human.
When my cat would lay on her back, I’d grab and hold her paw that she stuck in the air. Then I’d say “Donkey. Donkey. Hey Donkey! My ears are tied, and Donkey Donkey Donkey!”
Why would I say this? Because cats don’t speak english. You can say ANYTHING as long as it’s in a positive voice!
I once said “meow” in a positive voice and the cat looked at me as if I had just offended six generations of mothers.