@Linda Handelsman said
"email addresses do not match" and asked if I wanted to add the non-alias address
A Google Workspace email alias normally delivers into the primary Google mailbox, but it cannot be used to sign in as if it were a separate Google account. That would explain both the “email addresses do not match” message and why signing in with the alias fails.
What are you trying to accomplish in Outlook:
- Receive messages sent to the alias, or
- Select the alias in the From field and send messages from it?
If you only need to receive mail, messages sent to the alias should already appear in the primary Google account that is added to Outlook. Please send a test message to the alias and check whether it appears there.
If you need to send from the alias, that is a different issue. Please confirm whether, in Gmail on the web, the alias appears under Settings > See all settings > Accounts and Import > Send mail as, and whether you can successfully send from it there. That will confirm the Google Workspace side before determining whether Outlook for Mac can expose the same sender address.