If Taraweeh is considered an innovation because it was not practiced by the Prophet (s), why do we celebrate the Prophet's birthday if he never did so in his lifetime?
A short answer is, bid'ah is most strongly rejected when it comes to formal acts of worship. Performing mustahabb prayers differently from how the Prophet (S) taught it is a difference in formal acts of worship and is therefore inappropriate.
Although celebrating the Prophet's birthday can be considered devotional, it is not a shariah-prescribed act of worship like performing types of salat; it is more of a customary thing.
I am sure others will give a long answer! :)