Vectorize null_battery draws×layers loops (batched einsum Pearson; 50-100x)

Goal

Vectorize the draw/layer Python loops in src/explore_persona_space/analysis/null_battery.py into batched einsum/GEMM ops so a 1000-draw 4-null battery runs in minutes, not hours.

Motivation

#778's corrected-monitoring null battery (--n-draws 1000, raised from 200 by the statistics critic) ran 2+ hours at ~324% CPU. The module loops Python-level over draws (for d in range(n_draws) in perm_null_draws / randnorm_null_draws) and layers (r_per_layer calling scalar _pearson 28×), so wall time is op-dispatch overhead, not FLOPs (~1-2 TFLOP of actual math). Same overhead-bound many-cell pattern as #722 (.claude/rules/vectorize-many-cell-fits.md) — closed-form here, so pure numpy batching, no GD helper needed.

Sketch

• Stack K draw directions; projections for all draws×layers in one einsum('nld,kd->nlk') (or per-layer [n,d]@[d,K]).
• Batched Pearson: standardize target once + projections along n; mean-of-products gives all 28×K r values in one op.
• Permutation directions: diff-of-means for K shuffles as one [K,n_pool]@[n_pool,28*d] matmul. Randnorm: per-layer chol @ Z with Z [d,K].
• Within-condition r: batch draws×layers per condition (condition count is small).
• Keep the public API (perm_null_draws, randnorm_null_draws, r_per_layer, within_condition_r_per_layer) + seeds/draw semantics EXACTLY (regression test: same seed → same draws as the loop version on a small case). Memory guard: float32 direction stack, chunk K if needed.

Scope

src/explore_persona_space/analysis/null_battery.py + tests. Consumers (issue778/816 battery scripts) unchanged. NOT retrofit into live #778/#816 worktrees — main-only, for future batteries.