A while back I was interested in finding a joystick that connects by Bluetooth, I couldn’t find any. A recent search brought up a couple devices that are indeed joysticks, but not meant for flight.
I have linked below what I have found:
As you can see, these devices are incredibly more expensive than your average flight stick that most people buy. The way these are advertised, it looks like they are meant to be a pointer style joystick that is meant to replace a mouse or trackpad… which brings me to my next point.
Seeing that this the menu options you found are inside the Assistive Touch tab, if you were to connect a Bluetooth mouse, iOS would read it as a pointer device. That’s why you only see your joystick connection under that Assistive Touch menu. If Infinite Flight reads that joystick the way it reads any connected game pad device it should work.
In the end you would have a $300+ ‘wheelchair’ joystick (that’s the way these are being advertised) that has no thrust lever and almost no customization.
Before I end, I have found one cordless joystick that is the Logitech Freedom 2.4GHz Cordless Joystick. This is not Bluetooth but runs on A 2.4GHz frequency. What this does is the 2.4GHz receiver connects to a USB port on either a computer or a tablet and that receiver talks with the joystick. This is a good option for folks running IF on Android devices, but you still can’t connect a joystick directly into iOS devices, (for the purpose to use on IF) so this option wouldn’t work either.
Very few to zero options for a Bluetooth Joystick that would connect to iOS with Apple’s current restriction on 3rd party devices.