Patch for matplotlib#28123

Make Collection.set_linestyle normalize the empty string to 'None', and make Collection._bcast_lwls force linewidths to 0 if the dashes on_off_seq is None.

lib/matplotlib/collections.py

@@ -614,6 +614,8 @@ def set_linestyle(self, ls):
             ':', '', (offset, on-off-seq)}. See `.Line2D.set_linestyle` for a
             complete description.
         """
+        if ls == '':
+            ls = 'None'
         try:
             dashes = [mlines._get_dash_pattern(ls)]
         except ValueError:
@@ -705,6 +707,7 @@ def _bcast_lwls(linewidths, dashes):
             gcd = math.gcd(l_dashes, l_lw)
             dashes = list(dashes) * (l_lw // gcd)
             linewidths = list(linewidths) * (l_dashes // gcd)
+        linewidths = [lw if (dash[1] is not None) else 0 for lw, dash in zip(linewidths, dashes)]
 
         # scale the dash patterns
         dashes = [mlines._scale_dashes(o, d, lw)