Gmail automatically copies sent messages to Sent Mail, so that is the one to subscribe. Right-click the account in the Folder Pane, Subscribe..., Refresh, and subscribe Sent Mail (unsubscribe Sent). Also, in Account Settings, Copies & Folders, uncheck 'Place a copy in' to avoid duplicates in Sent Mail.

Gmail groups the special folders on the IMAP server (more precisely what Gmail calls system labels, which includes the special IMAP folders but also other Gmail labels) under a [Gmail] folder. Recent versions of Thunderbird hide that parent folder from the user in the folder pane, but you may still see the folder hierarchy on the IMAP server in other places.

In particular, if you go to the account Copies & Folders settings and select Other for sent messages, you'll see the special folders used by Gmail grouped under the [Gmail] folder there, and that's how you may know which is and select the folder that Gmail uses for sent messages.