Sounds like an interesting project. There are several things you need to figure out. Let’s break it down. Feel free to ask more questions and then show your results.
Streaming Connection Options and Cable Length Limitations
USB is the easiest and probably the best, but other people have used Ethernet. Check out this thread by @amoffat
This setup is with a physical connection with Ethernet.
Someone is back stage holding a THETA on the end of a stick. You can see how it looks with moving people.
This is another person using Ethernet.
The same person @Lau, also tested different lengths of USB and Ethernet.
You can see from that thread, that they looked at long USB cables of 20 meters with the THETA S, but ended up using Ethernet.
As the Ethernet system is likely too complex for your project, I would suggest trying a USB cable and posting your results.
If you want to try Ethernet, here is some additional information.
If you are transmitting to YouTube with Ethernet, you can use this plug-in and not use the camera Wi-Fi. The plug-in will automatically switch to Ethernet if you have the Ethernet active on the camera.