Make the pointwise 2M+P3 tendencies ForwardDiff-differentiable

[haakon-e]

Implicit (Rosenbrock-type) microphysics substepping needs Jacobians of the pointwise 2M+P3 tendencies w.r.t. the 8 prognostic species, so ForwardDiff.jacobian must work through bulk_microphysics_tendencies (logλ is held fixed). This PR does some groundwork to enable this.

• Modify P3State and Γ_incl to accept a mix of Dual and floating point arguments.
• Implement Dual method for SF.gamma_inc_inv (What about gamma_inc_inv's derivative ? JuliaMath/SpecialFunctions.jl#452) locally. Ideally this should be added to SpecialFunctions, and I might do so later, but adding here to move forward locally for now. The implementation uses a mix of analytical and central differences of the forward map.
• Ensure ice_mass_coeffs returns one tuple type (needed for efficient AD).
• Type early returns and fallback values across the 2M, NonEq, and P3 leaves by the promotion of all the arguments the result derives from (new Utilities.promote_typeof), so a caller mixing Dual and float arguments does not get a union-typed, heap-boxed return.
• Handle edge cases for sgs_weight_function (lower tail rounds 1 - a to 1, so atanh(-1) = -Inf) and SB2006 autoconversion (vertical tangent of τ^0.7 at zero rain), which previously could produce NaNs.
• Unrelated fix: get_distribution_logλ_from_prognostic called an undefined function.

I might try to differentiate through the logλ shape solve later; which needs ∂/∂a of the forward gamma_inc (JuliaMath/SpecialFunctions.jl#317).

Tests cover Jacobians at four regimes for both float types against per-row central finite differences, the gamma_inc_inv rule into the q = eps() tail, the regularised-ratio band, and that the touched functions stay concretely typed under single-Dual and all-Dual argument mixes.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 92.92%. Comparing base (ea430c0) to head (aa342a2).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #725      +/-   ##
==========================================
+ Coverage   92.74%   92.92%   +0.18%     
==========================================
  Files          56       56              
  Lines        2701     2728      +27     
==========================================
+ Hits         2505     2535      +30     
+ Misses        196      193       -3     

Components	Coverage Δ
src	93.77% <100.00%> (+0.17%)	⬆️
ext	69.47% <ø> (ø)

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[haakon-e]

This change is part of the following stack:

• Make the pointwise 2M+P3 tendencies ForwardDiff-differentiable #725 ◀
  • Add a Rosenbrock substepping mode for 2M+P3 #726
    • Add 1M AD-Rosenbrock averaged-tendency mode #731
      • Add post-solve per-process Rosenbrock tendency diagnostics #732
        • Add implicit-temperature Rosenbrock averaged-tendency mode #733
          • Make the quadrature scheme the configuration choice #728
            • Re-add diagnostic-Nc activation for the 2M scheme #729

_{Change managed by git-spice.}