Add cycle benchmarking with mid-circuit measurements

[jordanh6]

I'm going to be adding the mid-circuit measurement cycle benchmarking protocol from Pauli Noise Learning for Mid-Circuit Measurements, arXiv:2406.09299. This will also lead to support for cycle benchmarking of Clifford gates.

This feature would like to utilize built-in randomized compiling support (#313) (it will require randomized compiling of MCMs to be included, but I can help with that if needed).