wifi extnender

That $10 fee can cover up to 3 extenders so you could ask AT&T for another one or two to help coverage.

You could cancel that service and return the extender if you bought a third party extender (or wifi mesh system, my preference).  But if you want to keep the AT&T extender, yes, you'd still pay no matter what you do with third party equipment.

Not if you cancelled it. You can buy a 3rd pt extender, cancel the wifi extender with ATT and just use your own, that way you won't have to pay that 10 dollars indefinitely.

What wifi extender would you all recommend? I am switcing to AT&T in a couple weeks. My current ISP uses an Eero router so I purchased eero mesh extenders to work with it. Now I find out, after being told differently by AT&T when I signed up, my eero extender doesn't work with their system. If this is the case I am going to have to purchase a new extender. I am not tech savy so I am not sure what my best option at an affordable price would be.

You can use whatever system you want independently of the gateway.  If the Eero can run in access point mode, it would be simplest method.  Otherwise you give the Eero an IP passthrough  connection and will likewise work fine.