On Cowin portal I see an option to add passport details. Should I add the details? Will it be required while flying outside of India?

Yeah i guess govt has enabled those details to be viewed in the vaccination certificate.

It basically replaces Aadhaar with Passport Number in

ID Verified

field of the certificate, likely to ease the verification should you travel internationally.

yes, looks like it https://livefromalounge.com/how-to-link-passport-with-vaccine-certificate/