meta(distributed): multi-node and multi-GPU execution — backend API, IGG halo, tests, slab adjoint

[kylebeggs]

Umbrella for everything that makes a CartesianGrid operator run across more than one device or node. MDLA (single-node multi-GPU, CUDA-only) is done behind the _dist_scatter! / _dist_reduce! seam; what remains is the API to choose a backend, the multi-node backend itself, the tests that prove ≥3 partitions, and one perf gap on the slab transpose.

Sub-issues, in order

1. feat(api): explicit distributed-backend selection (MDLABackend / IGGBackend), mirroring AbstractJVPBackend #47 — explicit backend selection (AbstractDistributedBackend, MDLABackend, IGGBackend), mirroring AbstractJVPBackend. First: it is the entry point feat(distributed): ImplicitGlobalGrid halo backend for multi-node CartesianGrid #46 must implement against, and today a second extension defining prepare_distributed(::AbstractOperator, ::Integer) would be ambiguous.
2. feat(distributed): ImplicitGlobalGrid halo backend for multi-node CartesianGrid #46 — ImplicitGlobalGrid halo backend for multi-node. Carries the κ-ghost note from the PR feat(distributed): compact diffusion leaf on partition slabs #66 review (the IGG backend owes one setup-time exchange of the coefficient's Interface ghosts) and, from perf(algebra): constant-fold affine time-step operators (α·I + β·Laplacian) into one stencil pass #52, the comm/compute overlap idea: launch the interior stencil, run _exchange_storage! concurrently, then finish the boundary strips. Overlap is not to be built before a blocking exchange is measured.
3. test(ci): officially instantiate test/multigpu (>=3-GPU distributed tests) #30 — instantiate test/multigpu (≥3-GPU distributed tests). Upstream blockers cleared; also lifts the min(NGPUS_MDLA, 2) caps in test/mdla_gpu.jl.
4. perf(distributed): slab Diffusion adjoint runs the generic masked gather at ~5.7× the forward stencil #77 — slab Diffusion adjoint runs the generic masked gather at ~5.7× the forward stencil. Becomes a per-iteration cost the moment distributed reverse-mode AD lands.

Invariants that bind every sub-issue

• _dist_reduce! must remain the exact transpose of _dist_scatter! across ranks, including the ∂/∂κ scatter-add — this is the part with no equivalent in the IGG/ParallelStencil ecosystem.
• One halo exchange per operator application; coefficient exchanges belong at prepare time.
• No new core dependency: MPI/IGG live in ext/.

---

_{🤖 Beep boop — Claude drew the org chart; Kyle is not delegating to himself.}