I don't use Basic but I'll answer based on how it would work in Professional

enter taxpayers' email on the Federal Information Worksheet then change your HomeBase View to include a column for email addresses

Whose email address? Yours or the clients?

Basic does not have a tab for "homebase view"

the client's email address.  I want to show that in HomeBase.

You can't (at least not in 2021 or previous years).