[BREAKING] Transition from Tapir to Mooncake

[gdalle]

Warning

Breaking change: AutoTapir is no longer supported, replaced by AutoMooncake (see SciML/ADTypes.jl#89)

DI deps

• Replace Tapir with Mooncake, bump ADTypes compat

DI extensions, tests, CI

• Rename everything from Tapir to Mooncake
• Handle new Mooncake.Config (ping @willtebbutt)
• Implement multi-argument support
• Reactivate other tests

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 89.87342% with 8 lines in your changes missing coverage. Please review.

Project coverage is 98.43%. Comparing base (987ca87) to head (a95cd2e).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
.../ext/DifferentiationInterfaceMooncakeExt/onearg.jl	75.00%	8 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #500      +/-   ##
==========================================
- Coverage   98.45%   98.43%   -0.02%     
==========================================
  Files         106      106              
  Lines        4452     4471      +19     
==========================================
+ Hits         4383     4401      +18     
- Misses         69       70       +1     

Flag	Coverage Δ
DI	98.48% <89.87%> (-0.03%)	⬇️
DIT	98.31% <ø> (ø)

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[gdalle]

I think multi-argument support is operational, care to take a look? All you need to know is that:

• contexts can contain any number of arguments (including 0), wrapped in specific types like Constant <: Context
• one can access the actual data with unwrap, e.g. unwrap(Constant(c)) == c

[willtebbutt]

Largely looks good, just a couple of queries.

[willtebbutt]

Looks good from my perspective. I don't see how we could need to do anything else in this PR that is breaking, so if there is anything that's not been implemented optimally, we can revisit the details later on.