If the TV streaming is in 4K then it will almost certainly affect your gaming, but if that streaming is just 1080p then your gaming using a connection via a WiFi extender will probably be causing more problems. WiFi extenders are great for many things, but gaming isn't one of those things. If you have to connect over WiFi, see if connecting to the router directly is any better, and ideally, if you can get hold of a gigabit capable ethernet cable - the purists may not like the idea, you can get flat ethernet cables that are easier to hide!
*I certainly wouldn't suggest spending any money until you've tried the no-cost and low-cost options!
I only learn by making mistakes and owning up to them - boy do I learn a lot!
