[upstream-candidate] Hoist build_tree scratch vectors into depth-indexed members (base_nuts)

[sims1253]

Hoists the per-recursion-level locals in base_nuts::build_tree (p_init_end, p_sharp_init_end, rho_init, p_final_beg, p_sharp_final_beg, rho_final, rho_subtree, z_propose_final) plus transition()'s rho_extended into member scratch buffers, sized lazily on first transition (num_params x max_depth). Removes ~630 heap allocations per transition at tree depth 6 on hierarchical models.

Recursion safety: a node at depth d only touches slot d; children use slot d-1; outputs children write into the parent's slot are read only after the children return. z_propose_final is a per-depth ps_point stack — a single shared ps_point would be overwritten by the recursive call that receives it as z_propose.

Untouched: leaf z_propose assignment, transition-scope vectors, compute_criterion, integrator/hamiltonian internals, RNG call order. No arithmetic reordering.

Evidence (cmdstan 2.39.0; models blr, pilots, lsat_model, arma11, eight_schools_noncentered)

• Bit-identity: 3 models x 2 seeds x 4 chains vs stock: 24/24 CSVs byte-identical (modulo elapsed-time/file-path comments).
• callgrind (pilots, 40 warmup + 40 draws): memcpy/alloc instruction share 9.9% -> 6.7%; total Ir -6%.
• Wall-clock (warmup+sampling, 1000+1000, 4 chains, medians of 3 reps): geomean ratio patched/stock 0.931 (pilots 0.928, arma11 0.966, blr 0.888, eight_schools_noncentered 0.943).