As far as I know, “Escape” mode never made it to TF2 in any fashion, so whenever I get the urge for it, I crank up Team Fortress Classic and play with its healthy repertoire of Escape maps available. Also (unlike the TFC proper servers in my area) it still has a healthy playerbase today, which I link to at the end of this article and anyone who wants can go play even now.
At its core, the Escape mode is a cooperative game mode with only one team, composed entirely of Civilians. Together, your cadre of umbrella-wielding dudes tries to navigate a hazardous map of puzzles, pitfalls, and other perils to safety.