Yes, when I log in to my Microsoft account I see that I have purchased Office 2021 on the same day on which I got my MS office 2021 activated. That means if I want to reinstall MS Office 2021 on my new PC (after recovery) then I just need to access my Microsoft account and "install" from that account.
I guess I understood it right. So, there is no need for a product key, it is linked to my Microsoft account.
Thanks, Carlo.