What does it mean when they say up to 256 interpolation and 16 micro stepping for the TMC step sticks?
Higher microstepping numbers result in smoother movement.
However, printer control boards are limited in how many steps the can generate per second - as low as 10'000 steps/s on an 8-bit AVR board running Marlin.

To get the benefits of smoother microstepping, without adding load to your control board, TMC stepper drivers support interpolation between each step impulse coming from your control board, up to 256 different positions with which the stepper motor is driven.

You will still have to set up your firmware for the 16 "real" microsteps, the interpolation is only done on the stepper driver itself.