Hello,
You appear to be dealing with two separate issues.
Issue 1: Office 2021 on macOS Ventura
macOS Ventura 13 can only run an older compatible version of Office.
Microsoft ended support for Ventura after Office version 16.101, released in September 2025. Newer Office updates require macOS Sonoma 14 or later.
Since you have Office Home & Student 2021, first uninstall the current Office apps, then install version 16.101 using this installer:
https://officecdn.microsoft.com/pr/C1297A47-86C4-4C1F-97FA-950631F94777/MacAutoupdate/Microsoft_365_and_Office_16.101.25091314_Installer.pkg
After installation, try activating Office again with the Microsoft account originally associated with the Office 2021 license.
Issue 2: No access to the old email address
Is the inaccessible email address the Microsoft account associated with your Office 2021 purchase?
It is important to distinguish between the Microsoft account sign-in address and the recovery email address. Losing access to the email inbox does not necessarily mean the Microsoft account itself is unavailable.
Try signing in with the same Microsoft account and password. If Microsoft asks for a verification code, select Show more verification methods and check whether a phone number or alternate email address is available.
If you cannot access any of the listed verification methods, select I don’t have any of these. Microsoft will then allow you to replace the security information, but there is normally a 30-day waiting period before the new information becomes active.
This delay is a security measure designed to prevent someone from taking over an account by immediately replacing its recovery information. Unfortunately, Microsoft Support cannot bypass the waiting period.
Microsoft explains the process here:
https://support.microsoft.com/account-billing/-your-security-info-change-is-still-pending-or-you-can-t-access-this-site-right-now-microsoft-account-message-cbd0f64f-02d9-45d2-90c3-2375e5a72e52