Mail that is “on my Mac” vs gmail “all mail”

All Mail is the “Label” it uses for where it archives all of your email so it’s easier to harvest.

Mail maps that “Label” to the “Archive“ mailbox. Gmail can label a message with multiple labels. That doesn't translate very well to IMAP, which has messages in a single folder. You will see duplicates all over.

You should use Gmail in the web portal as it was designed for the idiosyncrasies of Gmail.

It should not be in both places unless you copied (not moved) the message. But since gmail does not really implement IMAP, I am not surprised that things don’t work correctly. Messages that are deleted tend to go to Archive instead of Trash, as another example of how gmail works sometimes. But at least messages that are On My Mac are really there, and separate from gmail.

dialabrain wrote:

FWIW, I have four active Gmail accounts. I've never had Mail automatically add emails to "Archive".

That can be if you mapped the Archive mailbox to something not on the server or you have disabled All Mail in IMAP.

I actually haven't changed any defaults until your post. What I did notice was Gmail webmail was keeping deleted emails in "All Mail", until I changed a setting to "Immediately delete the message forever".

FWIW, I have four active Gmail accounts. I've never had Mail automatically add emails to "Archive".