Please double confirm your SMTP server which could send the e-mail. Besides, a subscription can be just for you, or if you are a team admin, can be shared by everyone in the team.
If you are setting up a team subscription, try to change to a personal subscription first to check if it works. This will help to narrow down the issue.
To configure notifications, simply follow our official tutorial here-- Manage your notifications
For on-premises TFS, you must configure an SMTP server for team members to see the Notifications option from their organization menu and to receive notifications.
Please double confirm your SMTP server which could send the e-mail. Besides, a subscription can be just for you, or if you are a team admin, can be shared by everyone in the team.
If you are setting up a team subscription, try to change to a personal subscription first to check if it works. This will help to narrow down the issue.