Facade coming off wooden doors
Don’t use wood glue it will not normally adhere to the laminate.
Rubber cement / contact adhesive is a good method. I have a spray that is great for this it is made for putting sandpaper on sanding disks. But it’s just rubber cement in a spray can.
For Rubber cement contact adhesives to work they need to be applied and let dry until tacky then pressed together.
I suggest the spray in this case so there are no bubbles of adhesive but a thin coat allowed to get tacky then pressed together is how laminate countertops are done.
Once the contact glue , rubber cement is applied it should not come loose again so make sure to align the piece as once stuck it is almost impossible to remove without breaking.
I have laminate rollers to push things together but this size could be done with the palm of your hand just don’t use excessive glue.