Add ADTypes 1.0 compat

[gdalle]

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

ADTypes is about to release a breaking v1.0, so the task of updating downstream repos begins.
This is a test PR to see if there is anything to change here. From what I can tell, the only use of ADTypes in SciMLBase is through AbstractADType, which is still available, so we should be good.

However note that this PR is not yet testing with ADTypes v1.0, so we won't know for sure what happens. In particular, restricting ADTypes v1.0 to Julia v1.10 and above (as we decided in SciML/ADTypes.jl#40 (comment)) is probably very breaking throughout the ecosystem.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 4.86%. Comparing base (0ec4159) to head (4984f1c).
Report is 3 commits behind head on master.

❗ Current head 4984f1c differs from pull request most recent head 30e985f. Consider uploading reports for the commit 30e985f to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #674       +/-   ##
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- Coverage   40.84%   4.86%   -35.99%     
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  Files          55      55               
  Lines        4490    4443       -47     
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- Hits         1834     216     -1618     
- Misses       2656    4227     +1571     

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[gdalle]

@ChrisRackauckas thoughts on how to proceed here? I don't think we can really prepare draft PRs everywhere until ADTypes v1.0 is registered. We'd need to install ADTypes from the repo every single time, as well as all other dependencies (for instance SciMLBase), which means a huge chain of interlinked PR branches

[ChrisRackauckas]

I think it's fine to merge since this is just the interface, and thus it won't actually be used until the downstream users (currently Optimization.jl and NonlinearSolve.jl) allow it. This then isolates the problem to the downstream places where it's actually used, which should be fine.

[gdalle]

I guess this deserves a minor version bump?

[gdalle]

Hi! Now that SciML/ADTypes.jl#46 is done, if ADTypes v1 doesn't break CI for SciMLBase, would it be possible to release v2.34?