When I said pi isn't about circles I was meaning that it isn't primarily about circles. I am not trying to argue that it has nothing at all to do with circles. Clearly it does.

What I am saying is that the essence of sine and cosine is that they are solutions to f''(x) = -x, and the essence of pi is that it is the half-period of the sine function. And we can derive a Maclaurin series for that function purely based on the differential equation. We don't need to know that sine is a trig function to solve the equation.

The application to circles and trig could be viewed as secondary to this, because they are governed by the same differential equations.