Fix solver correctness and input-validation issues from code review

- Refuse the uniform contact model when the fills form multiple
  disconnected copper groups that each touch both terminals: the
  prescribed injection split is ill-posed and the grounded system was
  singular, silently returning garbage (e.g. negative gigaohms).
  connected_restrict now reports the component count; a power-balance
  backstop (SolverError) catches any other inconsistent solve.
- Connect via/pad barrels to the nearest fill copper within the pad
  footprint (+1 cell) instead of only the exact center cell, so
  thermal-relief spokes still stitch layers; barrels that reach fill on
  fewer than two layers are warned about. ViaLink gains pad_nm
  (extracted from the padstack, JSON-roundtripped).
- Validate dialog input on OK (layers, current > 0, cell > 0, parseable
  frequency, extra Cu >= 0) with an inline error instead of silently
  substituting defaults; parse_frequency raises on garbage; pipeline
  rejects i_test <= 0; choose_cell_size rejects non-positive overrides.
- Warn when a contact part is dropped by the connectivity restriction;
  floor instead of truncate in cell_of; correct the uniform-model
  summary line; drop an unused variable; refresh plugin.json wording.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

tests/test_geometry.py

@@ -51,6 +51,7 @@ def test_problem_json_roundtrip_v2(tmp_path):
          [([(0, 0), (10, 0), (10, 1), (0, 1)], [])]],
         rect1_mm=(0, 0, 1, 1), rect2_mm=(9, 0, 10, 1),
         contact1="L0", contact2="L1", vias_mm=[(5.5, 0.5)])
+    p.vias[0].pad_nm = 600_000
     f = tmp_path / "dump.json"
     save_problem(p, f)
     q = load_problem(f)
@@ -58,6 +59,7 @@ def test_problem_json_roundtrip_v2(tmp_path):
     assert q.electrodes1[0].contact == "L0"
     assert q.electrodes2[0].contact == "L1"
     assert len(q.vias) == 1 and q.vias[0].drill_nm == p.vias[0].drill_nm
+    assert q.vias[0].pad_nm == 600_000
     assert q.plating_nm == p.plating_nm
     assert np.array_equal(q.layers[0].polygons[0].outline,
                           p.layers[0].polygons[0].outline)