Model pads and vias as KiCad places them

Measured against KiCad's own pads on the TerraHawk rc4 power stage:

- Back-side parts kept their pads on F.Cu (32 pads). Mirror the copper
  layer for a back-side part.
- Pad outlines were copied unrotated (29 pads on rotated parts). Place the
  outline through the same chain as the pin: pin rotation, back-side
  mirror, part rotation. Oval pads, a path with a width, came out as a
  zero-height sliver; pad them out by the aperture.
- Multi-shape padstacks used the first shape; use the largest.
- Footprint-level keepouts were parsed but never placed. KiCad exports a
  mounting hole's plated ring that way, so the router could not see it.
- Vias were sized like a trace (0.25 mm square for a 0.6 mm via), and every
  remaining short and clearance error was a via. Read the size from the
  DSN's via padstack and use it in all three engines; the grid engine now
  reserves the cells a via's copper reaches.

With these the exact and room engines route that board with no shorts,
clearance or other DRC errors. Pins now carry their component reference.

src/freeroute/route/pipeline.py

@@ -45,6 +45,25 @@ def _via_padstack(dsn: DsnBoard) -> str:
     return dsn.via_padstack_names[0] if dsn.via_padstack_names else _DEFAULT_VIA
 
 
+def _via_half_board(dsn: DsnBoard, scale: int) -> int | None:
+    """Half the via pad's size in board units, from the DSN's via padstack.
+
+    None when the DSN names no via padstack with a shape, so the engines fall
+    back to their old estimate.
+    """
+    padstack = dsn.padstack(_via_padstack(dsn))
+    if padstack is None or not padstack.shapes:
+        return None
+    half = 0.0
+    for shape in padstack.shapes:
+        if hasattr(shape, "diameter"):
+            half = max(half, shape.diameter / 2)
+        elif len(getattr(shape, "coords", [])) >= 4:
+            xs, ys = shape.coords[0::2], shape.coords[1::2]
+            half = max(half, (max(xs) - min(xs)) / 2, (max(ys) - min(ys)) / 2)
+    return round(half * scale) or None
+
+
 def route_dsn_board(
     dsn: DsnBoard,
     *,
@@ -62,6 +81,7 @@ def route_dsn_board(
     clearance_board = round(_rule_clearance_dsn(dsn) * scale)
     result = route_board(
         board,
+        via_half=_via_half_board(dsn, scale),
         trace_width=width_board,
         clearance=clearance_board,
         layers=layers,
@@ -130,6 +150,7 @@ def route_dsn_board_exact(
     clearance_board = round(_rule_clearance_dsn(dsn) * scale)
     exact = route_board_exact(
         board,
+        via_half=_via_half_board(dsn, scale),
         trace_width=width_board,
         clearance=clearance_board,
         layers=layers,
@@ -175,6 +196,7 @@ def route_dsn_board_rooms(
     clearance_board = round(_rule_clearance_dsn(dsn) * scale)
     rooms = route_board_rooms(
         board,
+        via_half=_via_half_board(dsn, scale),
         trace_width=width_board,
         clearance=clearance_board,
         layers=layers,