Then you have a few options,
One is start ordering displays and try to get one that works, the remaining could be used for other personal projects.
Order a soldering iron with a bigger display already, I know most of them have tiny screens.
Try to modify the code for yours to accept a different screen, I believe firmware for this STM32 soldering irons are on line but you would need to reverse engineer the controller board to be sure the µC and connections are the same for the firmware you get or modify the code so it fits. You could download the original firmware so you can go back if that doesn't work.
Watch the data bus and try to make sense of the data to find a proper replacement.
After reading the post again I see you are trying to go for a smaller display, I don't exactly understand why you are doing this, but couldn't the seller send a replacement display for you to mock around, you probably need to tell them your display isn't working but the iron does heat up and all that. If you have a second one you could even try to solder a 30 pin OLED directly to the PCB they had sent you, or reverse engineer the display PCB and make a new one for yours, it doesn't looks as simple as drop in but it seems like you are having trouble to find one.
JS