Here’s an Imgur link that has more photos.
Basically, it slides into a slider on the post and the four rods hold the crossbar in place.
It depends what you’re playing on it, for sure. I Can get a couple hours of GameCube or PS2, and a few hours of older games. I mostly use it for the former, though I’ll occasionally use it for platformers that need more precision than the Analogue Pocket’s dpad Can provide. It’s still a mushy dpad, but much less prone to false diagonals than Analogues.
You might look into repairing the joystick you have. I recently had a similar issue with my 360 controller after it sitting in storage for many years and a good contact cleaning got it working again.
If that doesn’t work, depending on your level of confidence, you could measure the pin pitch and note termination style and see if you can find a replacement joystick module to solder in somewhere. Maybe it used the same footprint as another controller, and you can drop it in and have it work.
Either way, good luck. I hope you succeed!