I think this is exactly what is going on. Gmail doesn't use IMAP folders in the traditional sense, it uses labels. For something to appear in your "Sent" folder, it only has to show your email address as the sender. Since it's quite common for spammers to use your email address as the "From" in spam messages sent to you, Gmail automatically throws it in your Sent "folder" by way of a label.
I freaked out at first when my Fastmail account started getting spammed seemingly by my old Gmail account (I no longer use Gmail but I kept the account active and forwarded to Fastmail to catch anyone I forgot to update with the new address). I logged into Gmail and immediately changed my password, made sure I didn't have any third party app access, and turned on 2FA.
After seeing this HN piece and reading through the first few messages in the Google product forum, I realized it was typical spam that was breaking through Google's spam filter and freaking everyone out due to Google's handling of the Sent folder/label.