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>

fill_resistance/geometry.py

@@ -87,6 +87,7 @@ class ViaLink:
     z_top_nm: int
     z_bot_nm: int
     kind: str = "via"                         # "via" | "pad"
+    pad_nm: int = 0                           # pad/annular diameter; 0 = unknown
 
     def spans(self, z_nm: int) -> bool:
         return self.z_top_nm - 1 <= z_nm <= self.z_bot_nm + 1
@@ -287,7 +288,8 @@ def problem_from_json(d: dict) -> Problem:
         vias=[
             ViaLink(x=int(vd["x"]), y=int(vd["y"]), drill_nm=int(vd["drill_nm"]),
                     z_top_nm=int(vd["z_top_nm"]), z_bot_nm=int(vd["z_bot_nm"]),
-                    kind=vd.get("kind", "via"))
+                    kind=vd.get("kind", "via"),
+                    pad_nm=int(vd.get("pad_nm", 0)))
             for vd in d["vias"]
         ],
         electrodes1=(