refactor(solver): dedup factorization caching and cross-DB dep helpers

[ccomb]

Summary

A readability pass over SharedSolver.hs that removes duplicated logic without changing behaviour.

• Factorization caching deduped. The lazy MUMPS factorization was computed-and-cached in two near-identical blocks (solveWithSharedSolver, ensureFactorization). Extracted computeAndStoreFactorization so the precompute + store lives once; the dense-solver fallback stays scoped to the first-solve (cache-miss) path exactly as before.
• Shared dep-demand helpers. The per-root dep-demand → demand-vector conversion was copied byte-for-byte in three resolvers (resolveDep, resolveDepContribs, and Service.resolveDepWithSubs). Extracted prepareDepDemandVecs, plus depDbsOf for the "DBs referenced at this level" set.
• Semigroup CrossDBSolution. mergeSolutions is now foldl' (<>) — same summed inventory and base-first / BFS-ordered scalings as the hand-written version.
• Named map types. Introduced SupplierDemands / DepDemands aliases in Matrix (where the type is produced) and used them across the affected signatures, replacing the verbose nested-Map spelling.

We deliberately stopped short of unifying the two dependency-graph walks (inventory vs. contributions) behind a generic interpreter: it barely reduces line count, would rely on a K=1 invariant the types don't enforce, and can't absorb the third walk in Service.hs.

Test plan

• ./gen-version.sh && cabal build — clean (only two pre-existing, unrelated API/MCP.hs warnings).
• cabal run lca-tests — 1107 examples, 0 failures, 1 pending.
• Rebased onto current advanced_haskell; rebuilt and re-ran the full suite green on the rebased tree.