refactor(diffusion): consolidate the eddy-diffusivity pipeline and diffusive-flux application

[haakon-e]

Consolidates the diffusion code in two layers: how eddy diffusivities are computed, and how diffusive fluxes are applied.

Coefficient layer. Extracts the TKE → mixing length → Prandtl → eddy viscosity/diffusivity chain, previously duplicated at seven sites, into a single ᶜeddy_diffusivities! function. Callers supply the mixing-length output field and optional K_u/K_h output fields, preserving each site's scratch slots and lazy or materialized policy; the closure inputs (grid_scale, buoyancy_gradient) pass through unchanged. The implicit-Jacobian scheme dispatcher is renamed eddy_diffusivity_coefficients! → ᶜimplicit_diffusion_coefficients! to distinguish it from the closure chain. Migrated sites: the vertical and horizontal EDMFX SGS diffusive fluxes, the vertical and horizontal updraft diffusion, the TKE tendency for both EDMF models, and the diffusion Jacobian coefficients.

Flux-application layer. Adds two shared zero-flux boundary-condition divergence operators (ᶜdiffdivᵥ, ᶠdiffdivᵥ_u₃, next to the existing operator constants in abbreviations.jl) and two lazy helpers (ᶜdiffusive_flux_divergenceᵥ, ᶠtotal_enthalpy_gradientᵥ), then migrates the five vertical diffusion sites that rebuilt these per function — vertical Smagorinsky–Lilly, vertical AMD, vertical_diffusion_boundary_layer_tendency!, the EDMFX grid-mean SGS diffusive flux, and the EDMFX updraft vertical diffusion — one commit per site.

Behavior-preserving. The coefficient-layer extraction reproduces each site's original expression, and every flux-application commit is bit-for-bit identical to its parent. The dynamics test group (Prognostic equations, Tracer/mass transport consistency, EDMFX horizontal diffusive flux) passes on this branch, and a new unit test (test/diffusion_operators.jl) pins the shared operators and helpers, including the diffusive-flux sign, at Float32 and Float64.

Scope and limitations. The diagnostics that recompute the closure fields lazily (edt, evu, edth, evuh) are deliberately not routed through the new function, which mutates scratch; unifying them needs either a lazy variant or cached diffusivity fields. A behavior-changing correction to the vertical-diffusion tracer scaling, surfaced by this refactor, is deferred to a follow-up PR. Unifying the tendency functions themselves (a per-direction driver over a declarative field table) is out of scope here.

[haakon-e]

This change is part of the following stack:

• feat(edmfx): add horizontal component to the EDMFX SGS diffusive flux #4657
  • feat(edmfx): add horizontal diffusion of prognostic EDMFX updrafts #4659
    • refactor(diffusion): consolidate the eddy-diffusivity pipeline and diffusive-flux application #4669 ◀

_{Change managed by git-spice.}

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📖 Docs preview for this PR: https://clima.github.io/ClimaAtmos.jl/previews/PR4669/