Cleanup regex compiler operators and operands source (#10879)

Cleans up the `regcomp.cpp` source to fix class names, comments, and simplify logic around processing operators and operands returned by the parser. Several class member variables used for state are moved or eliminated. Some member functions and variables are renamed. Cleanup of the parser logic will be in a follow-on PR.

Reference #3582
Follow on to #10843

Authors:
  - David Wendt (https://github.com/davidwendt)

Approvers:
  - Vyas Ramasubramani (https://github.com/vyasr)
  - Yunsong Wang (https://github.com/PointKernel)

URL: #10879