I think this is an issue with how Gmail/GSuite communicate with Mail.app. When I use my iCloud account, the sent messages folder works fine. It’s just my GSuite account that exhibits this problem. I assume that eventually, Apple will figure out the tag that’s causing IMAP to break and the emails will appear in the sent messages folder again.
In the meantime, the temporary workaround I came up with was to create a smart mailbox consisting of emails sent from my address. It’s not a perfect fix — the preview pane shows my name on the top of every messages, so I can’t scroll through and see the message recipients. To find a message, I have to search for the recipient, and change the “from” to “to”. But for now, at least I have a folder with sent messages.
I’m going to post this same message on a couple of other threads. I’m not a dev, so I can’t submit a radar. I tried submitting a couple of emails through the beta program over the summer, but they obviously didn’t have any effect. Maybe if there are enough complaints, one of the websites that covers apple will write a post . . .