Raise Mooncake compat floor to 0.5.36 (fix Downgrade resolution)

[ChrisRackauckas-Claude]

Replaces the Mooncake = "0.4, 0.5" union with a single floor at the latest, Mooncake = "0.5.36", in every Project.toml that declares a Mooncake [compat] entry. Dropping the old 0.4, 0.5 union stops the downgrade min-resolution from being able to pin an ancient Mooncake — the "limit to latest Mooncake" fix for the promotion-caused Downgrade Unsatisfiable wall.

Raised floors

File	Old floor	New floor
Project.toml (root, weakdep)	0.4, 0.5	0.5.36
test/downstream/Project.toml (full dep)	0.4, 0.5	0.5.36

Root package version patch-bumped 3.31.0 -> 3.31.1 (narrowing a weakdep [compat] floor is a patch-level change; no public-API change). test/downstream/Project.toml is an unnamed test env, so no version bump there. Only [compat] Mooncake lines were touched — the [deps]/[weakdeps] UUID entries are unchanged.

Verification — resolves_at_min = TRUE (observed)

Reproduced the downgrade min-resolution with the actual julia-actions/julia-downgrade-compat downgrade.jl (current main, incl. #49/#50/#51 merged-test-deps + [sources] handling) on Julia 1.12, cloning Resolver.jl exactly as CI does:

• Root . (the CI invocation: projects=".", mode=deps) — Successfully resolved minimal versions for . (exit 0). Mooncake is a weakdep here, so it enters the manifest only as a DifferentiationInterface extension reference, not a version-pinned dep; the resolve succeeds regardless.
• test/downstream/Project.toml (Mooncake is a full [deps]) — Successfully resolved minimal versions (exit 0). Mooncake pins to 0.5.36 (was 0.5.25 under the old 0.4, 0.5 floor — the current registry + merged compat constraints from ModelingToolkit etc. already prevented an ancient 0.4.x even before this change).

So on the current tooling the Resolver-capacity Unsatisfiable wall does not reproduce here; the floor-raise resolves cleanly at minimum versions in both projects and pins Mooncake to the intended 0.5.36 where it is a real dependency. resolves_at_min = true; no dependency on #52 for this repo.

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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.