Hi @Zurab Sajaia .
As you have mentioned, it does sound like the other account is being stored somewhere. Azure AD services use cookies to automatically sign in, and I've definitely faced the issue you described before. I would recommend doing the deep logoff with both of these links, in addition to the one you already shared:
https://login.microsoftonline.com/logout.srf
https://login.live.com/logout.srf
You can also sign out of all devices via the Microsoft 365 admin center, or ask your admin to do this for you. https://help.protectedtrust.com/sign-a-user-out-of-all-office-365-apps-and-sessions
If there's a fresh browser that you've never used to sign in, you can use that to verify if this is happening due to the credential storage and try signing in with the new browser. Normally clearing the cache should work but there have been times when I've been able to resolve this only by using a totally new browser.
I would recommend trying the troubleshooting steps in this article, and if you are still having this issue after trying those, I would be happy to raise a support request for you.
Let me know if this helps.
Thanks,
Marilee