It’s unusual that the middle side button (the Wi-Fi change button) does not cause the blue LED or the Green LED to flash. This could be a hardware problem, possibly with the button itself. Can you contact the seller and ask them if there were any known problems with the Wi-Fi?
If you sign up for the partner program (free to join), you can put the camera into developer mode, then use Vysor and a USB cable to apply a factory reset.
Depending on your technical knowledge and motivation, it may be too much of a hassle. However, it may be a path forward. backup all your images to your computer before you apply a factory reset.