They won’t allow you to use regular TOTP alone. You always have to link a phone, even for Google Workspace. It sucks!
This is not true. In some organizations I work with they only allow Security Keys on Google Workspace, you can't even use TOTP. It's possible to disable SMS and Phone verification, but if you allow TOTP then Google Prompt is also automatically allowed.
Neither my Google Workspace account nor my personal Gmail account has a phone number.