I'm sorry to hear that you're experiencing this issue. To access your Microsoft account on a different device, you need to update your security information and configure Microsoft Authenticator again, since the app is linked to each individual installation, much like a banking app. You can regain access using the Authenticator app on your previous device, restore your accounts from a compatible cloud backup, or register a new Authenticator installation through your account's security settings. If you have full access to your Microsoft account on your computer, please visit https://account.live.com/proofs/manage/additional and check whether you can manage your security information. If so, add and verify your new authentication method before removing the old Authenticator connection.
However, if your access on the computer is limited, you will need to follow a different process. From that computer, open the same link and try signing in with your current password. If you're prompted to verify your identity through an email code or Microsoft Authenticator, select Sign in another way and check whether another verification method is available. If none of the available methods can be accessed, select I don't have any of these and follow the instructions. Depending on your account's security configuration, you may be offered the option to replace your security information, which requires a 30-day waiting period before the changes take effect. Please note that an existing session on your computer does not necessarily provide full access to security settings. These are the available approaches to consider, depending on your current access and the recovery options offered for your account.