Office 365 newly purchased is not launching on my Big Sur Mac? What can I do?
One easy thing is to use a browser (other than Safari) and go to https://portal.office.com and make sure your license is set up.
Depending on which of the many versions of Office was sold to you, you might want to start with Microsoft subscription support to know which level and version of the programs you purchased so you can activate and sign in correctly. The applications are all the same, but the license you bring to the app enables the features your account provides.

https://support.microsoft.com/en-us/home/contact

Once the licensing is clear, then you can make sure you’re signing in to the apps and they pull the same license as your online check allows.