I want to connect my phone to my desktop (running manjaro-i3) to share the internet from my ethernet connected desktop to my phone. How do I do this?
That depends on your phone really. I have an iPhone, can’t speak for android. On iPhone, it must be connect to WiFi first, then turn on Personal Hotspot(Personal Hotspot may be Carrier dependent, you might have to pay for it, I don’t know). You can choose the password for your hotspot here also. Next go to Manjaro, select WiFi, look for the name of your iPhone(usually it’s iPhone), connect and enter password. As far I know it’s not possible to use Bluetooth with iPhone to get internet.
Edit: misread your post. I don’t know how to connect internet from computer to phone.
Blueman provides a GUI for getting that working.