feat: add infrastructure for initialization of different problem types

[AayushSabharwal]

Requires SciML/SymbolicIndexingInterface.jl#109

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.

[AayushSabharwal]

Requires SciML/ModelingToolkit.jl#3258 for testing

[AayushSabharwal]

Can the failing downstream test be changed to a <=? It passes locally, not yet sure why it fails CI

[ChrisRackauckas]

Yeah that's fine. I guess you expect that on average it will go to a better local minima but it doesn't always... not a great test.