There was no hype in that story about the Battle of Brooklyn. The British fully expected to take Washington and his forces in Brooklyn and it was miraculous that they escaped to Murray Hill, Manhattan across the East River.
In October the British fleet was set to sail down Lake Champlain and capture Fort Ticonderoga and link up with their counterparts in New York City by sailing down the Hudson and basically capturing the entire Hudson River. But the brave Benedict Arnold fought a suicidal naval battle after hiding his makeshift fleet behind Valcour Island and attacking the British from behind after they passed the island. Arnold almost got killed (many of his men had to swim to shore after their ships were shot out from under them) but he forced the British northern forces to spend another 11 months trying to push south of the lake, by which time the politics of New York State had changed and the loyalists in the Albany area were ready to fight the British on farmland near Saratoga.
Anyway, after escaping to Murray Hill (which is where UN employees now live) Washington had tea with Mrs. Murray who was apparently an attractive rich widow. Apparently he dallied amost too long because the British had crossed into the Wall Street area the morning after the Americans escaped in a fog from Brooklyn and the Brits were moving up the west side highway to try to encircle his forces yet again. Whenever I am on the west side highway, I think about how the America was saved because American troops ran fast to the north that day.
Sadly it has been long forgotten the vital part New York played in the Revolutionary war. Yes, it started in Boston(tea party)and lexington/concord, finally finishing up in jamestown VA 5 years later; but it was NEW YORK where the main action took place. It was Hamilton that put manhatten on the road to becoming NYC but if Washington had known what a liberal snake pit it would become he might have hung it up right there and stayed even longer at tea w/Mrs Murray.