Does console and phone need to be on the same WiFi for console streaming?

The MAC spoofing function is there specifically for this problem; you sign in to the WiFi on another device, a phone for example, then once authenticated, enter the MAC from the phone on the console. The WiFi then thinks that the consoke is the phone.
You will likely encounter issues if the phone and console attempt to be connected to tge WiFi at the same time. So use a device that doesn't need wifi too often!

Well, your console has to connect to the Hotspot. The Hotspot only provides WiFi, and does not connect to devices itself.

Set up your Hotspot to be visible. If you use a smartphone as Hotspot, be aware that you can NOT use Bluetooth as tethering method. The phone needs to use WiFi to share it's cellular connection.

Some modern phones are able to bridge a WiFi connection, but usually, if you set up a WiFi hotspot on your phone, the connection to WiFi gets disconnected, and the phone connects to the Internet via it's cellular network, and shares that connection via WiFi.

Go to your console's network settings and let it search for WiFi networks. Does your Hotspot SSID (Network Name) show up in the list?

If not, check your phone settings.

If the SSID shows up on the console, connect to it, and provide the Password that the phone provides (or that you set up in your phone for the Hotspot).

Depending on your cellular data plan, it might not be permitted to use Laptops, PCs or consoles via cellular hotspot. In that case contact your phone provider.

Also be aware, that multiplayer through such a hotspot is usually problematic.

Have you tried it on Wifi with cellular off

You need to register the console, with both the phone and the Xbox on the same local network before it will work.

Does your wifi work with all other devices other than the Xbox?

If you think there's something wrong with the Wifi card in your console, then you can easily check it by enabling hotspot on your phone, and then use that hotspot as wifi on your console.

Same exact issue here. Everything streams fine on my phone or tablet over WiFi and on both my wired PCs.

My One is set up with all of the appropriate ports open on the router it's wired to (I've even tried putting it in the DMZ) and the console reports an open NAT and a good connection. I have no issues streaming Netflix or YouTube, just Twitch.

The issue does tend to clear up if I let it play for a while and it doesn't happen every time, but probably 95% of the time.