If your phone is used as a hot spot then the Roku is using your mobile data to serve its internet right?
So you have stopped the Roku using the BT internet, it will leverage your phones 4G/5G instead, this indeed would stop TV steaming effecting your gaming.
I thought the same, I turned off the WiFi connection on my phone and the roku ate my data, I turned it back on and it used the Internet off my router, it's bizarre and it works and I'm baffled but happy.