Make CheckInit the default for ODEs and DAEs: breaking

[Ickaser]

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

Context

Bulk of the discussion happened in #2514 , see particularly this comment . This is a separate pull request because I did a clumsy job rebasing that branch and filled the Git history with all the commits since November.

#2554 worked on this in a non-breaking way, including exporting BrownFullBasicInit and ShampineCollocationInit from ODENonlinearSolve.

Changes

Currently this is a very simple pull request.

This will require some documentation, which I haven't done yet.
Note to self: probably needs it at

• https://github.com/SciML/DiffEqDocs.jl/blob/master/docs/src/types/dae_types.md
• https://github.com/SciML/DiffEqDocs.jl/blob/master/docs/src/solvers/dae_solve.md
• Possibly add a file like https://github.com/SciML/NonlinearSolve.jl/blob/master/docs/src/release_notes.md with some upgrade notes?
• https://github.com/SciML/DiffEqDocs.jl/blob/master/docs/src/tutorials/dae_example.md

[ChrisRackauckas]

I think this looks good for v7