MS Office is unable to correctly show my licence

I owned Office 365 with few university logins. After my relationship with universities ended I bought MS Office 2021 licence. I claim the product key with my private MS account - so I would have universities accounts and my private in the list of users in for example Word (will be used as example from now on).

After a while university licences ended but the private one (with Office 2021 product key registered) somehow was not able to "licence" Office. Now Word at the title claim to be "unlicenced" but when I went for "Files -> Accounts" I clicked at my private account it shows (in red) that I do not have licence for "Enterprise Office 365" I clicked button here, click to change the account, click I have product key (as one of the help showed) and everything was clear there - no red sign, but title still showed "unlicenced" product. I tried to solve this but installing Office from install file downloadable after writing my product key, but got same result.

After that I decided to uninstall all Offices from my computer (it turns out there was 365, 2021 and several languages versions). The results was the same. After that I tried to log off one of my university accounts and the behaviour change. It showed me that I have had 5 day trial of 365 on my private account (which I never want nor claim nor checked anywhere). Nevertheless it shows unlicenced product, in "Files -> Accounts" shows again in red "Microsoft 365 Enterprise App" but when I click activate the product, I choose to wrote the product key, nothing change. I log off from all of my university accounts, reinstall Office, restart computer, start Word as a administrator and nothing changed.

How can I finally persuade Office to start working as 2021?