On Thunderbird I prefer to store sent messages in "Inbox" rather than "Sent" in order to subject them to the same "delete or archive" workflow as received emails, primarily to enable deleting Emails with large attachments before they accumulate.
A common solution for this is to automatically CC or BCC yourself, but this requires adding third party extensions in Gmail, which also raises questions about whether this will actually work for e.g. Emails sent from the mobile app.
Can it be achieved with builtin tools?
Posted as Q&A after I've found a solution.