Fix GaussAdjoint with ZygoteVJP for in-place ODE functions

[ChrisRackauckas-Claude]

Fixes #1282

Summary

Previously, GaussAdjoint with ZygoteVJP() would fail when used with in-place ODE functions, throwing a MethodError: no method matching fiip(::Vector{Float64}, ::Vector{Float64}, ::Float64) because it was calling the in-place function f(du, u, p, t) with only 3 arguments as if it were out-of-place f(u, p, t).

Changes

• Added check for in-place vs out-of-place ODE functions using SciMLBase.isinplace()
• For in-place functions: Uses Zygote.Buffer to allow mutation during forward pass while remaining differentiable
• For out-of-place functions: Keeps existing behavior
• Added comprehensive tests for both in-place and out-of-place cases

Technical Details

The key insight is using Zygote.Buffer which enables Zygote to differentiate through in-place functions by:

1. Allowing controlled mutation during the forward pass
2. Returning an immutable copy via copy(du_buf) for the backward pass
3. Letting Zygote build the pullback for the values, not the mutation operations

Testing

• ✅ New test file test/gauss_zygote_inplace.jl with comprehensive coverage
• ✅ Tests both in-place and out-of-place ODE functions
• ✅ Verified with the original failing example from issue Adjoint fails when using ZygoteVJP #1282
• ✅ Tests pass on Julia 1.10.10 (LTS) and 1.11.7

Test Output

Julia version: 1.11.7
✓ Basic solve with GaussAdjoint succeeded
Computing gradients...
✓ Gradient computation succeeded!
  du0 = [-44.39290603871477, -8.472174656702613]
  dp = [0.1944861128441424, -158.5656423260541, 75.24591831397161, -345.0325681954895]

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