Raise Mooncake compat floor to 0.5.36 (fix Downgrade resolution)

[ChrisRackauckas-Claude]

Summary

Narrows the Mooncake [compat] entries from "0.4, 0.5" to a single latest floor "0.5.36" in every Project.toml that declares Mooncake, so the Downgrade lane can no longer pin an ancient Mooncake (the "limit to latest Mooncake" fix for the promotion-caused Downgrade Unsatisfiable wall).

Raised floors

File	Mooncake role	Old floor	New floor
lib/NonlinearSolveBase/Project.toml	weakdep (NonlinearSolveBaseMooncakeExt)	0.4, 0.5	0.5.36
test/Adjoint/Project.toml	direct test dep	0.4, 0.5	0.5.36

Bumped NonlinearSolveBase 2.31.3 → 2.31.4 (a [compat] narrowing on a weakdep is a patch-level change, not a public-API change). test/Adjoint has no version field (test env), so nothing to bump there. Root Project.toml declares no Mooncake.

Verification (downgrade min-resolution actually resolves)

Ran the actual julia-actions/julia-downgrade-compat downgrade.jl (current HEAD, with the merged-test-deps create_merged_project path) + StefanKarpinski/Resolver.jl (HEAD 9353ca5) on Julia 1.12.6, reproducing the CI downgrade lanes on the two Mooncake-carrying projects:

• test/Adjoint (Mooncake in direct [deps]/[compat], non-merged --min=@deps path — the true Mooncake→Resolver path): Successfully resolved minimal versions, selecting Mooncake 0.5.36 (the new floor).
• lib/NonlinearSolveBase (Mooncake weakdep-only, merged [extras]/targets.test path): Successfully resolved minimal versions. Mooncake is not in [extras]/targets.test, so it is never promoted into the merged [deps] fed to Resolver.jl.

resolves_at_min = true — the downgrade min-resolution succeeds after the bump.

Note: on the current Resolver.jl HEAD 9353ca5 + Julia 1.12, this repo's test/Adjoint graph resolves at min even with the old "0.4, 0.5" floor (resolving to Mooncake 0.5.1), so the earlier fleet-wide Resolver/Mooncake Unsatisfiable wall does not reproduce for this repo's dependency-graph shape here. The floor-raise still holds the min-resolution to the latest Mooncake and does no harm.

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Please ignore until reviewed by @ChrisRackauckas.

[ChrisRackauckas-Claude]

Closing. Verified locally (ran the action's own downgrade.jl on the identical commit CI failed on) that raising the Mooncake compat floor does NOT fix the Downgrade lane. The failure is julia-downgrade-compat@v2 merged mode promoting all ~13 weakdep AD backends (Mooncake, Zygote, ForwardDiff, DifferentiationInterface, …) to hard deps and running Resolver.jl --min on the joint graph — which is registry-snapshot-dependent (flips UNSAT↔SAT as those packages release) and independent of Mooncake's version. This PR also unnecessarily narrows Mooncake compat. Real fix is julia-actions/julia-downgrade-compat#52 (do not promote weakdeps in merged resolution). Superseded — closing.