refactor: rewrite HomotopyContinuationProblem to target NonlinearSolveHomotopyContinuation.jl

[AayushSabharwal]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Add any other context about the problem here.

[ChrisRackauckas]

HomotopyContinuationProblem isn't documented in NonlinearSolve.jl right? Can you write up the appropriate docs for it? Since we should make sure this is fully completed.