The joystick button functions are configurable. Switching video feeds is unrelated to the autopilot (so can’t be set using the autopilot button parameters), but QGC provides a set of extra button functions that it can either handle locally or send a direct MAVLink message that a system may be able to handle.
I believe you’re after the “Next Video Stream” / “Previous Video Stream” functions, although I did just try those (and the “Next Camera” / “Previous Camera” ones) and wasn’t able to get them to work. I’m pretty sure they worked previously, so I’ve asked internally in case we know why that would have changed.
So you’re aware, QGC does also include support for sending custom MAVLink commands to the vehicle, but that’s unrelated in this case.