Hello, Yuki Sun,
The issue cannot be reproduced with any other message. When I use the browser to access Gmail, the message appears only in All Mail, not Sent. It was a message to an external party, not to myself. Synchronizing the folder does not solve the problem.
I am confused by your suggestion to disable "Do not save copies of sent items". It will impact all sent messages and duplicate outgoing messages on the Gmail server.
I resubscribed to All Mail and it is taking a very long time to build up again. Note that in addition to resubscribing, I need to manually use Outlook to recreate the All Mail folder, as it disappeared after unsubscribing and syncing.
After All Mail folder was rebuilt, it still did not contain the message, which I can still see in All Mail when accessing Gmail via a browser.