I have had this problem for a long time. Since I just searched for an email in Aqua-Mail that I deleted from the Gmail inbox in the Gmail Trash and did not find it, I would finally like to solve the problem.
I use Gmail on Mac and on Aquamail. All folders synchronize wonderfully.
When I delete an email on the Mac, it goes to the Gmail Trash (in German "Papierkorb") and is also displayed in the "Deleted" folder in Aqua-Mail.
However, when I delete an email in Aquamail, it goes to the "Deleted" folder, but then does not synchronize with the Gmail Trash. The deleted email can only be seen in Aquamail "Deleted".
Ask for help on how to set this up correctly.