Raise Mooncake compat floor to 0.5.36 (fix Downgrade resolution)

[ChrisRackauckas-Claude]

Summary

Raises the Mooncake [compat] floor from 0.5.15 to the latest registered 0.5.36 in every Project.toml that declares Mooncake compat. This is the "limit to latest Mooncake" fix for the promotion-caused Downgrade Unsatisfiable wall: the old 0.5.15 floor let the downgrade resolver try to pin an ancient Mooncake, which Resolver.jl could not satisfy.

Raised floors (both 0.5.15 -> 0.5.36)

File	Section	Old	New
Project.toml	[compat] Mooncake (weakdep)	0.5.15	0.5.36
test/AD/Project.toml	[compat] Mooncake (dep)	0.5.15	0.5.36

Only [compat] Mooncake lines were touched; [deps]/[weakdeps] UUID lines are untouched. Root package version bumped 3.87.0 -> 3.87.1 (a compat narrowing is a patch-level change; a Mooncake weakdep floor is not public API). test/AD/Project.toml has no version field (test sub-env), so no bump there.

Verification (resolves_at_min = true)

Ran julia-actions/julia-downgrade-compat@v2.5.1 (downgrade.jl, includes the #51 [sources]-strip) on Julia 1.12 at minimum versions, faithfully reproducing the CI downgrade job:

• test/AD (where Mooncake is a real [deps] entry fed to Resolver.jl): Successfully resolved minimal versions — Mooncake pinned to exactly =0.5.36, alongside LinearSolve 3.87.1, Enzyme 0.13.35, JET 0.11.0, ForwardDiff 0.10.38. No Unsatisfiable.
• root . (mode deps, merged extras+targets.test resolution, matching Downgrade.yml): Successfully resolved minimal versions for . (with extras). Mooncake stays a weakdep here (not in root [extras]/[targets].test), so it is not promoted/resolved on the root job; the Mooncake-carrying resolution is test/AD, verified above.

So the floor-raise alone does clear the Mooncake downgrade resolution (resolves_at_min = true); the Resolver-capacity wall does not persist for this repo after the bump.

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Please ignore until reviewed by @ChrisRackauckas.

🤖 Generated with Claude Code

[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.