What seems idiosyncratic is actually evidence of care and trust. Cats communicate a lot through smells and pheromones, which are particularly intense on the animal's anal gland.
Not every cat likes to be petted there; some find the touch on their backside unpleasant. Similar to dogs, cats sniff the buttocks of their fellow cats when they get to know each other. When a cat is ready to greet, it turns its head away, lifts its tail and bottom, and presents itself to the other cat. At the same time, the animals show that they are in a peaceful mood and that they do not pose any danger. If you see two cats smelling each other's butts, they may be trying to say 'I'm here to play with you' or 'I've got a toy for you to show you.' If the cat turns its backside toward you while stroking it, it means you are doing everything right. However, you should be careful with your touches, especially because the area of the body is so sensitive.