Is Eid shortbread an innovation (bidʿah)?

Bid‘ah (innovation) has two meanings: a linguistic meaning and a Shar‘i (legal) meaning. The linguistic meaning is to originate or invent something, and it can be good or bad depending on the thing invented. For example, making Eid cakes is a linguistically good bid‘ah. As for the Shar‘i meaning, bid‘ah in this sense is nothing but misguidance, based on the Prophet’s (peace and blessings be upon him) sayings: “Whoever introduces into this matter of ours that which is not from it, it is rejected,” and “Every bid‘ah is misguidance.” Making Eid cakes does not fall under this meaning.