Show a busy window while the solve runs

On OK the dialog closed and nothing appeared until the figures did,
which on a real board is minutes of looking like the plugin did
nothing. Put a small always-on-top window up for that stretch: the
stage now running, elapsed seconds, and Cancel.

Qt only repaints while the event loop runs and the solve owns the
thread, so the window pumps events itself - from inside the CG/AMG
iteration callback, which is where the time actually goes. That is
also where Cancel is noticed. The state is module-level because the
tick happens several frames deep in scipy/pyamg, and threading a
handle through those signatures for a progress bar is not worth it;
it stays inert until start(), so the standalone runner and the tests
are unaffected.

The window covers the figure work too, not just the solve: laying out
labels and writing four PNGs at full DPI is seconds on a real board -
10-15 of them on a large one - and closing before that left the same
silent gap one step later.

fill_resistance/pipeline.py

@@ -4,7 +4,7 @@ from __future__ import annotations
 
 from pathlib import Path
 
-from . import config, plots, raster, report, solver
+from . import config, plots, progress, raster, report, solver
 from .errors import UserFacingError
 from .geometry import Problem
 from .solver import Result
@@ -20,8 +20,8 @@ def run(problem: Problem, outdir: Path | None, show: bool = True,
     if i_test <= 0:
         raise UserFacingError(f"Test current must be > 0 A (got {i_test:g}).")
     h = raster.choose_cell_size(problem.copper_bbox(), len(problem.layers))
-    print(f"rasterizing {len(problem.layers)} layer(s) at cell size "
-          f"{h / 1000:.1f} um ...")
+    progress.stage(f"rasterizing {len(problem.layers)} layer(s) at cell "
+                   f"size {h / 1000:.1f} um ...")
     stack = raster.rasterize_stack(problem, h)
     print(f"grid {stack.shape2d[1]}x{stack.shape2d[0]}x{stack.nlayers}, "
           f"{int(stack.masks.sum())} copper cells, {len(problem.vias)} "
@@ -30,8 +30,8 @@ def run(problem: Problem, outdir: Path | None, show: bool = True,
     e1, e2 = raster.electrode_masks(stack, problem)
     parts1, parts2 = raster.electrode_partition(stack, problem)
 
-    print(f"solving @ {i_test:g} A"
-          + (f", {freq_hz:g} Hz" if freq_hz > 0 else " DC") + " ...")
+    progress.stage(f"solving @ {i_test:g} A"
+                   + (f", {freq_hz:g} Hz" if freq_hz > 0 else " DC") + " ...")
     result = solver.run_solve(problem, stack, e1, e2, i_test, freq_hz,
                               contact_model, parts1, parts2)
     for prefix, pcs in (("P", result.part_currents1),
@@ -51,6 +51,7 @@ def run(problem: Problem, outdir: Path | None, show: bool = True,
         except Exception as e:
             print(f"overlay push failed: {e}")
 
+    progress.stage("rendering figures ...")
     figs = [
         (plots.fig_raster(stack, e1, e2, problem, result), "1_raster_map"),
         (plots.fig_potential(result, stack, e1, e2, problem), "2_potential"),
@@ -58,5 +59,5 @@ def run(problem: Problem, outdir: Path | None, show: bool = True,
          "3_current_density"),
         (plots.fig_power(result, stack, e1, e2, problem), "4_power_density"),
     ]
-    plots.save_and_show(figs, outdir, show=show)
+    plots.save_and_show(figs, outdir, show=show)   # closes the window itself
     return result