test+docs(two_stage): CI-review P1 - methodology suite asserted the old lstsq warning

tests/test_methodology_two_stage.py::test_singular_omega0_warns_and_falls_back
still matched "lstsq" in the fallback warning (my sibling sweep covered
tests/test_two_stage.py but missed the methodology file); now matches
"falling back to sparse LSMR". Also the stale spillover.py
re-factorization note describing the removed dense toarray() fallback
(review P3).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Lbd6nqWmg4snvvBmegwqiw

Author: igerber

diff_diff/spillover.py

@@ -1597,9 +1597,8 @@ def _build_butts_fe_design_csr(
     supported warn-and-drop fit), the input code arrays can be sparse —
     e.g. ``unit_codes = [0, 1, 3, 4]`` with code 2 dropped. Building
     ``X_10`` on the raw codes would materialize an all-zero FE column at
-    index 2, forcing ``sparse_factorized`` onto the dense
-    ``lstsq``/``XtX_10.toarray()`` fallback unnecessarily (large-memory
-    path on big panels). To avoid this, re-factorize via
+    index 2, forcing ``sparse_factorized`` onto the certified sparse-LSMR
+    fallback unnecessarily (a warned degraded path). To avoid this, re-factorize via
     :func:`pd.factorize` on entry to compact the code space to
     ``0..n_unique-1`` (no-op when codes are already contiguous; mirrors
     the column-space convention of ``TwoStageDiD._build_fe_design``).

tests/test_methodology_two_stage.py

@@ -409,8 +409,8 @@ def test_singular_omega0_warns_and_falls_back(self) -> None:
         """A rank-deficient Stage-1 design (a period observed only among treated
         obs -> its time FE is unidentified in Omega_0 -> X_10'X_10 singular) makes
         the sparse factorization in the GMM variance fail; the code must emit a
-        UserWarning and route to the dense lstsq fallback, still returning a
-        finite SE."""
+        UserWarning and route to the certified sparse-LSMR fallback, still
+        returning a finite SE."""
         rng = np.random.default_rng(_BASE_SEED_VAR + 9)
         rows: List[Dict[str, Any]] = []
         uid = 0
@@ -432,8 +432,8 @@ def test_singular_omega0_warns_and_falls_back(self) -> None:
                 panel, outcome="outcome", unit="unit", time="time", first_treat="first_treat"
             )
         assert any(
-            "lstsq" in str(w.message) for w in caught
-        ), "expected the dense-lstsq fallback warning under a singular Omega_0"
+            "falling back to sparse LSMR" in str(w.message) for w in caught
+        ), "expected the sparse-LSMR fallback warning under a singular Omega_0"
         assert np.isfinite(res.overall_se)
 
     def test_bootstrap_scores_use_exact_residuals(self) -> None: