We would like to inform you that most likely you are not completely drying the housing after thoroughly rinsing your housing.
I'm not sure how to parse this. I dunk my camera in the rinse tank, work all the buttons while submerged in freshwater, then take it out and let it dry. When I'm on the Smiling Seahorse, they have an air tank in the camera room with a hose and nozzle attachment, allowing me to dry the housing quickly with a high-pressure stream of dry air. After a trip, I soak it for 24 hours and let it dry again. I'm not sure how different drying procedures can affect zoom gear operation.
We would also like to let you know that we can see exactly what the problem is, based on your photos you have a missing rubber band on the upper left side of the housing (inside) the photo is attached to this email. Exactly because of the lack of this rubber band the camera is not standing correctly and because of it zoom gear does not work and also because of it the flash does not open correctly. Please find this part and replace it.
They're referring to a flexible rubber piece that is inserted into that plastic piece on top left. It slides onto the T-shaped part in the middle. They sell it as a spare part -
Spare part (Top left corner pad for a6xxx Salted Line)
However, that whole assembly gets in the way of inserting/removing the camera, and I have... misplaced mine years ago. In my experience it is absolutely not needed for proper operation of the camera. You could try removing the plastic part that holds it, like I did, and see if that helps with your issue.
@Barmaglot what do you mean exactly by stiffen the gear?
The gear is made of rubber, and is thus somewhat flexible. You could take a sheet of stiff plastic, cut out a ring matching the size of the gear where the '16-50mm' label is, and glue it onto the gear. This would give it extra stiffness and prevent it from deforming out of shape. Just an idea - I haven't tried it myself, as I haven't had a reason to.
Also, is it just a trick of the light, or do you have a section of about four or five teeth on your gear outright missing? If so, you should replace it - if that section gets on the driving cog, it will lose all contact and you will lose the ability to zoom. and while you can try to avoid that section (you don't need the entire 360 degrees to go through 16-50mm zoom range), hitting it by accident can ruin a dive. I don't see spare 16-50mm A6xxx housing gears offered on their website, but you might be able to get one by contacting support. If not, I have a spare set of 16-50mm+10-18mm gear from my old housing that leaked; let me know when you're back in Thailand.