The only shot fired was by the LE person who "assassinated" the woman climbing through the window.
Siege is such a ridiculous word to use for this event, pure agitprop.
Siege : a military blockade of a city or fortified place to compel it to surrender
In history, sieges were events of many days duration, if not months.
This protest event delayed the ratification of the electoral college vote by a few hours.