Hey abycats,
Have you tested this with another email service provider (if you have another one)? This also depends on the type of email server you have with Gmail. For example, IMAP or POP email servers. You may need to look into your Gmail settings as well.
Please look at this article that talks about how to Change Mailbox Behaviors preferences in Mail on Mac
You can focus on the section that talks about the Draft mailbox to confirm that you do not have the "On my Mac" option selected. If you continue to experience the same issue, we recommend you reach out to Google support for additional assistance.
Cheers!