Raise Mooncake compat floor to 0.5.36 (fix Downgrade resolution)

[ChrisRackauckas-Claude]

Raises the Mooncake [compat] floor to the latest release (0.5.36) in every Project.toml that declares Mooncake compat, so the strict Downgrade min-resolution stops pinning an ancient Mooncake ("limit to latest Mooncake" fix for the promotion-caused Downgrade Unsatisfiable wall).

Raised floors

File	Old floor	New floor
Project.toml (root, [compat])	0.5.25	0.5.36
docs/Project.toml ([compat])	0.5	0.5.36

Root package version bumped 7.113.0 -> 7.113.1 (a [compat] narrowing on a weakdep is a patch-level change). No [deps]/[weakdeps]/[extras] UUID lines were touched.

Verification (resolves_at_min = true)

Reproduced the downgrade min-resolution faithfully on Julia 1.12 with julia-actions/julia-downgrade-compat@v2, the exact path the centralized Downgrade.yml takes: the root has [extras] + [targets].test, so downgrade.jl runs the merged-extras resolution with mode=deps, --min=@deps, allow_reresolve=false semantics. In that path Mooncake is promoted weakdep -> dependency ([ Info: Promoting Mooncake from weakdep to dependency in merged project) and fed to Resolver.jl.

Result with the raised floor:

[ Info: Running resolver on merged project (extras) for . with --min=@deps
[ Info: Successfully resolved minimal versions for . (with extras)

Resolver.jl resolved successfully at minimum versions (exit 0, no Unsatisfiable), pinning Mooncake = 0.5.36 in the emitted Manifest.toml. So resolves_at_min = true — the floor-raise alone is sufficient here; the Resolver-capacity wall does not persist at current master.

(Control run with the old 0.5.25 floor also resolves at current registry state, pinning Mooncake 0.5.25 — so this change does not regress resolution and correctly lifts the floor to the latest.)

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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.