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Hi there,
Thanks for your reply.
According to your provided screenshots, it seems like there is a conflict between the university account's license and the version of Office you are using - Microsoft Office LTSC Professional Plus 2021.
Regarding on your Office apps, you might need to contact the original seller (who provided you the Product key) as this product was failed to validate itself from the server.
Additionally, your Windows is also having issue with its activation state, you might need to fix it first as it could affect Office apps as well.
Please try to access this link and review your given license from your university: https://portal.office.com/Account#subscriptions and provide me the screenshot if possible.
To summarize this, the Office license you are having on your computer is having issue with the validation, you might need to contact back the original reseller who provided you this license. Fixing Windows Activation could possibly fix the Office Product Activation as well.
Sincerely,
Austin H - MSFT | Microsoft Community Support Specialist