The answer to the question in the title looks as if it is common sense but before I discuss it, it should be said that not all cats circle all the time when settling down to snooze or sleep. They tend to fiddle around a bit when they could more efficiently just plonk down. Living in a comfortable human home and having well used places where a cat sleeps all the time there is no need to circle and fiddle around to ensure that they are going to be comfortable. The know the ropes. And in any case cats are known to sleep almost anywhere.
Have you seen those internet photos of cats sleeping on clothes hangers and other strange places? Here is one example:
It is more peculiar than that because in my experience cats seem to like sleeping on cables and lumps that might crisscross a nice comfy duvet. Or, at least, cats don’t mind sleeping on what look like uncomfortable objects to humans.
First-hand experience tells me that domestic cats have a good tolerance for what looks to humans to be uncomfortable bedding. But circling before snoozing must be about getting into a position which feels comfortable, and I think the biggest factor in feeling comfortable is the direction in which they are facing when they have settled and not the smoothness of the bedding.
They have an instinct for facing the right direction when settled. And the ‘right direction’ must be one which provides them with the most reassurance. In turn this must mean a good line of sight for what is happening as most of the time that cats are sleeping it is not REM sleep but light snoozing. REM sleep is rapid eye movement sleep. It’s deep sleep. But other than a relative short period or periods of REM sleep cats can be fully awake and moving within about 2 seconds while they are ‘sleeping’ if they hear a strange sound that spells trouble and which might threaten them. Their ears are picking up sounds all the time while enjoying non-REM sleep.
Thinking about it, domestic cats circle on their bedding or their human’s lap to instinctive feel the safest direction to face. However, once settled and getting into the mood for REM sleep, domestic cats often change their position to one which might make them more vulnerable. However, they have decided that the place where they are sleeping is safe and therefore can change position without feeling anxious. Sometimes they are positioned very vulnerably but they are at home and I guess that knowledge overrides their wild cat instinct to be safe when sleeping.
That is my assessment having considered it while typing this. I mean, at the end of the day, it must be about feeling emotionally comfortable and in the mood for REM sleep. As mentioned, I don’t think physical comfort is a major factor except for heat. They normally like a source of warmth under, over or directed at them, which also makes them feel more relaxed and in the mood for sleep.
Below are some pages on cat sleep. There are many more pages on feline sleep. Feel free to search for them using the custom search.