I found this Google’s page on the recommended setting on Mac OSX Mail.app, and I am trying it on. It still kept Sent folder in the left pain, but I see only the items that I sent from Mail.app after the change and no historical sent items. I’m not sure if this works for me, but I can see all sent items in web Gmail so I’ll keep it this way for a while more.
From the Mail menu, click Preferences > Accounts > Mailbox Behaviors
Store draft messages on the server > do NOT check
Store sent messages on the server > do NOT check
Store junk messages on the server > checked
Delete junk messages when > Never
Move deleted messages to the Trash mailbox > do NOT check
Store deleted messages on the server > do NOT check