Do you have stock or custom firmware? Stock: pairing is NOT posible. Custom: i do not know.

You might want to look in to these or this (both have the ability to use a wide aray of modern bluetooth controllers

I’m a big fan of the 8bitdo converters! They are great (the best?) way to use modern controllers on retro devices.

There is only one compeditor at this moment... brook’s wingman ... brook’s converter can have an external powersuply (might solve your issue?)