The grid was blank because lanes and zones segments have null row_index/col_index.
The old code assumed all layouts were grid-type and collapsed to 0×0.

- Grid layouts: keep the spreadsheet-style row/col selector view
- Lanes layouts: render as horizontal strips (label + cell side by side)
- Zones/custom layouts: responsive card grid (no row/col concept)

Layout type is now read from Facility::activeLayout (new HasOne relationship)
with a null-safe fallback to row_index detection. Segment cell HTML extracted
to _segment-cell.blade.php partial to avoid triplication.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>