Windows won't detect my Gamepad / Joystick

You could try to follow this guide of connecting it to the Pc. Essentially, it seems that for this controller, even with wireless connection, you need to press and hold the home button, in order for it to be able to connect. That might be also the case for a Bluetooth connection. Normally, almost any Bluetooth device first need to pair with the Pc before it is usable.

I don't know about connecting an Xbox controller wirelessly to Windows 10, because Microsoft recently removed the drivers that allow you to do so from their website. You could download drivers that somebody else has made themselves, but that increases the risk of breaking the software of your PC/Laptop and controller from 1 to 10. However, connecting your controller using a charging cable/USB cable is, for sure, a reliable way to use your controller on your PC/Laptop. I don't know how many functions you can carry out, but I know for sure that if you're in a Roblox game and you plug in your controller, it'll convert all the controls if the game is compatible for consoles and is available to play on console. The same can be said for Fortnite and it works just as fine and feels like playing just like it does on console but with a smaller screen. I have not tried anything else and do not wish to make assumptions and give you information that may not be true.

You should try connecting it with a cable. If that doesn't work, try restarting the computer. See if it works on your Xbox if you have one. If it does not, maybe your controller is just broken. If it works on the Xbox, it is possible that your computer port is broken. If this does not work, you should try youtube or microsoft support.