Replacing "AC Control Panel" in 2011 Prius?

Hi all, newbie here so please forgive me if this is not the right way to ask this question.

About two months ago, our A/C stopped blowing cold air and was only hot (and the AC light stopped coming on if you pressed that button). We took it to an independent mechanic who is well known in the area and they said the "climate computer" needed to be replaced and we would need Toyota dealership to program that.

We took our 2011 Prius to the dealer for service, and they quoted us $1200 (later gave me a breakdown of $375 for labor, the rest for part). In our paperwork, they wrote that we need an "AC Control Panel." If you search around, you don't really find that as a part (though I've found similar things like "HVAC Control Module" or "Climate Control Panel"). Has anyone ever heard of this?

We're planning to buy the part elsewhere (even the Toyota Parts site is cheaper) and then going to ask them to install it (since apparently only the dealership can program it).

Thanks in advance for any advice/information. It's been frustrating.