Upgrade ADTypes to v1

[gdalle]

Upgrade ADTypes to v1.0 for the sparse backend types only (nothing yet about the coloring and sparsity detection infrastructure).

Supersedes #294

Main changes

• Bump Julia compat to v1.10, adjust CI
• Remove everything "1.9-specific" in tests
• Replace every AutoSparseForwardDiff(...) (construction) with AutoSparse(AutoForwardDiff(...))
• Replace every AutoSparseForwardDiff (dispatch) with AutoSparse{<:AutoForwardDiff} (be careful with type parameters like {C})
• No need to define AutoSparseEnzyme anymore
• Use manual trait for dispatch on mode in sparse_jacobian_cache(ad, args...; kwargs...) = sparse_jacobian_cache_aux(mode(ad), ad, args...; kwargs...). Add implem for ForwardOrReverseMode which checks if we're dealing with Diffractor or Enzyme (not hit by tests for some reason 🤔)
• Replace _get_colorvec(alg, ad) with _get_colorvec(alg, mode(ad))

Questions

• I bumped the version to 2.19 because ColPrac says dependency compat upgrade is not breaking. However, the ADTypes API did leak into the SparseDiffTools API through the docs, so I'm not sure if this deserves a 3.0?
• In the update process for ADTypes v1.0, we should go from the roots of the dependency tree to the leaves. However, that means downstream integration tests are bound to fail at first. Is that okay?
• This PR does nothing to integrate the coloring and detection infrastructure of SparseDiffTools inside the generic framework introduced by ADTypes v1.0. I think this would be a breaking change, so I suggest doing it separately

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 57 lines in your changes are missing coverage. Please review.

Project coverage is 0.06%. Comparing base (a96de04) to head (1365d5e).
Report is 2 commits behind head on master.

❗ Current head 1365d5e differs from pull request most recent head 6f001e2. Consider uploading reports for the commit 6f001e2 to get more accurate results

Files	Patch %	Lines
src/highlevel/forward_or_reverse_mode.jl	0.00%	12 Missing ⚠️
src/highlevel/common.jl	0.00%	11 Missing ⚠️
src/highlevel/coloring.jl	0.00%	9 Missing ⚠️
ext/SparseDiffToolsEnzymeExt.jl	0.00%	6 Missing ⚠️
ext/SparseDiffToolsZygoteExt.jl	0.00%	5 Missing ⚠️
src/highlevel/forward_mode.jl	0.00%	4 Missing ⚠️
ext/SparseDiffToolsPolyesterForwardDiffExt.jl	0.00%	2 Missing ⚠️
ext/SparseDiffToolsSymbolicsExt.jl	0.00%	2 Missing ⚠️
src/SparseDiffTools.jl	0.00%	2 Missing ⚠️
src/highlevel/finite_diff.jl	0.00%	2 Missing ⚠️
... and 1 more

Additional details and impacted files

@@            Coverage Diff            @@
##           master    #295      +/-   ##
=========================================
+ Coverage    0.00%   0.06%   +0.06%     
=========================================
  Files          24      25       +1     
  Lines        1366    1463      +97     
=========================================
+ Hits            0       1       +1     
- Misses       1366    1462      +96     

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[gdalle]

@ChrisRackauckas this is ready for a first pass. Not sure if the missed lines in Codecov are my fault or not.

[ChrisRackauckas]

Looks good!

[avik-pal]

Can we do a major version bump here for safety since we are dropping ADTypes pre-1.0?

[avik-pal]

I know ColPrac doesn't require it, but NonlinearSolve is very tightly coupled rn with sparsedifftools..

[gdalle]

I was wondering whether to include more changes to SparseDiffTools first. Basically I only did the backend part, but the new ADTypes also has infrastructure (supertypes and functions) for sparsity detection + coloring, which SparseDiffTools could extend. On the other hand that would be super super breaking, which is why I didn't do it in the current PR (my priority was getting things to work)