How to make a bind to rotate the camera using additional buttons on a gaming mouse?

Question

Mouse

Good day to all.
Recently I encountered such a problem as the need to somehow bind additional features in one toy to additional mouse buttons. My mouse is a special gaming mouse from RAZER, something like this.

As you can see, it has additional buttons on the side that are responsible for any additional actions that can be set in them. Moreover, the mouse is both a mouse and a keyboard at the same time, this is also visible in the image.

The mouse buttons themselves are banal buttons 1-2-3-4-5-6-7-8-9, and 0, 'minus' and '=' for buttons 1-12, respectively, of the usual overtext keyboard. The point is that I need to bind the camera rotation to these buttons ( namely, the mouse camera, not the cursor!) in a certain direction, i.e. how to imitate real human activity with button binds, for example, so that when you press button 1 on a gaming mouse, the camera rotates to the left as if I am doing it now with my mouse, 3, right, 8 down, 2 up, etc.
I scoured for a very long time and found just such a program. It's called Joy to Key.

She was perfect for my needs. For fun, I connected an old WINGMAN gaming device.

And oddly enough, the program is fully consistent with my research. When the joystick was tilted in different directions, the character's camera in the game turned Up, Down, Right and Left, it was possible even with acceleration up to 10x or bind the buttons on the joystick itself to rotate the camera, everything was on schedule. It looked very impressive. It only remained to figure out how to do the same with the mouse, so that when you click on certain buttons, the mouse camera rotates in certain directions.
But here's the problem!
Joysticks of this kind are perceived by the computer as separately connected game controllers with a similar menu.

And that's why the Joy to Key program works only with game controllers, but flatly refuses to perceive my game mouse with buttons as a game controller, i.e. does not see it as a "joystick with buttons".
In this case, my question is. How can I make the mouse buttons rotate the camera in different directions? Perhaps you can somehow "redirect" the signals of the mouse buttons to some virtual controller and then send them to Joy to Key? Or maybe it's worth going down a completely different path and doing it in a simpler way?
I’ll tell everyone who will offer me mouse macros or something like that right away, I have already tried a lot of macros, but I could not find one that would have sufficient functionality to provide a similar level of return. Although if someone knows a macro that could successfully implement such a task, I will be very grateful.
Thanks in advance.