It’s normal territorial behaviour, and afaik the signaling of their tails is the complete opposite, means they don’t understand each other. Also, have you put two random cats in the same room, maybe one both of which see it as their home?

Dogs just accept you into their pack. Ideally as the leader. Doesn’t mean they will, and many dogs won’t see you as superior. So they won’t be friendly if you act up. Cats just accept you in their territory. Because you provide food, hopefully. They may not accept other people in their territory.

Dogs do that too.

Cats wouldn’t sleep through, otherwise they wouldn’t have survived till now, but how would you hear a soft meow in your sleep? Our cat slept in our bed, wherever she wanted, and we noticed when she got up.