Is the recording feature greyed out when you are using Teams Web client?
Does anyone else have the same problem in your organization?
If the above issues are ruled out, We recommend you check if you meet these requirements. The following steps show how to check Teams configuration:
1.Please check your Teams license. Do you have one of the Office 365 E1,E3,E5,A1,A3,A5,Microsoft 365 Business Premium, Business Standard or Business Basic license?
You could sign in to Microsoft 365 admin center and click Users->Active users->More actions->Manage product license to check it.
2.Please check if you have enough storage in OneDrive or SharePoint Site.
3.Please check user role in Teams meeting. Anonymous users, guests, federated users and attendees have no permission to record meetings. For more details about roles permission in the meeting recording, you could refer to this link's table.