refactor: update for MTKv9

[AayushSabharwal]

I'll separate this PR out into another one that contains changes independent of v9

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.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 40.84%. Comparing base (a65ef30) to head (d4f90fd).
Report is 1 commits behind head on master.

Additional details and impacted files

@@             Coverage Diff             @@
##           master     #685       +/-   ##
===========================================
+ Coverage    8.65%   40.84%   +32.18%     
===========================================
  Files          31       31               
  Lines        2506     2522       +16     
===========================================
+ Hits          217     1030      +813     
+ Misses       2289     1492      -797     

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[AayushSabharwal]

The type-piracy removal is now in #689 so it can be merged independent of MTKv9

[ChrisRackauckas]

Does this still need to be a draft?

[ChrisRackauckas]

Test failure.

[AayushSabharwal]

MOI tests pass locally, I'm not sure why it doesn't resolve here. MTK probably doesn't pass because it isn't using the local OptimizationMOI

[Vaibhavdixit02]

The downgrade MOI one fails because you have removed 8.74 here but not in Optimization.jl's project.toml

[ChrisRackauckas]

Passes now!

[ChrisRackauckas]

The docs failures look real.

[AayushSabharwal]

Docs are probably failing because It's using OptimizationMOI v0.1.16. Bumping MTK compat makes it use v0.1.9 which is weird.

[AayushSabharwal]

So I can fix compat, but CI doesn't checkout the subpackages (specifically OptimizationMOI) so they won't build here

[AayushSabharwal]

Also docs doesn't have compat for the latest version of

• OptimizationPRIMA
• OptimizationSpeedMapping
  And OptimizationQuadDIRECT requires a different registry entirely

I'm trying to build docs locally by bumping compat for the first two packages and deving all the packages except QuadDIRECT. If it builds, should I also update CI?