Claude helped: Add a new example options file based on new format

Had Claude help in adding comments after I used the auto-converter script on things and manually updated all of the comments. It helped create a better documented options file that'll hopefully be easier for new users to parse and see how to implement things. Although, I still need to add some features such as some new solvers and actually let people define the preconditioner but shouldn't be too bad...

Author: rcarson3