People who promote the idea of 'bid'ah hasanah' give examples of Salatut Taraweeh in Jam’ah, and compilation of Qur’an in one Mus’haf. So how do we classify the above two examples. Please explain.

Both cannot be taken as bid’ah hasanah, because the bid’ah means a practice in deen which was not present before and innovated in Islam, whereas the mentioned both practices were not new in Islam. Taraweeh prayer was led by Prophet (ﷺ) in Ramadan and it’s not a bid’ah. There is a proof from ahadeeth in which Prophet (ﷺ) led the sahaba in taraweeh prayer. Secondly, it’s also evidenced that sahaba were used to write the Qur’an in Prophet’s (ﷺ) time. At the time of Abu Bakr (رضى الله عنه) they had just compiled it in a book format and as per Prophet’s (ﷺ) Hadeeth, he (ﷺ) said to follow his sunnah and his sahaba’s sunnah. So this proof to follow the sahaba is not called innovating in islam.