To me one sat is ₿ 0.00000001. But I am not against moving to sat denominated way of writing. One bitcoin is then written as (sat symbol)100,000,000.
If only we had a different symbol for SATs. Like ‘S’ with two stripes through it, but will probably look too much like a $ sign. As you say that could be confusing.
Newbies will probably get confused if we use the bitcoin symbol interchangeably. So if we are to use it for sats it should be fully adopted.