I would recommend eero
I would recommend an eero.
https://www.amazon.com/dp/B07WGJ8ZD3/ref=cm_sw_r_cp_api_i_T3uzFb34K2B70
You can buy an additional eero that matches your setup through this link.
also, is it as simple as buying the right extender and then hooking it up in the app? How do I know if i need to hardwire the extender which I think I can do, but it would be really difficult to run a wire to the exterior garage
Correct, you'd add the new eero through the app. As long as the new eero is close enough to another eero (any one) for a strong enough signal to perform wireless backhaul, then you shouldn't need to hardwire it. The app should help tell you if your placement is good enough or not for wireless during setup.