If they are performing the repair on their own premises, then they will be replacing the whole Top Case Assembly which includes the Keyboard, Trackpad, Speakers, Palmrest, and the Battery plus the Touchbar on the Touchbar models so that part is not unexpected to me. The battery is attached to the underside of the palmrest with really strong adhesive. Unless the prices are much higher in that region, then I'm guessing they are quoting you an incorrect price for the battery replacement. Yes the Top Case Assembly is really expensive (about $450 for a non-battery repair when the AASP exchanges the defective part with Apple) and even more expensive if the tech is not quoting an exchange price for the part. Apple has a battery only repair price for this part which is about the price I mentioned on the last post (again this price may vary by region). Apple provides a lower part cost for battery replacements as people would really complain about paying such a high price for a consumable item.
Is there another AASP you can go to for another quote or even an Apple Store? Click on the "Contact Support" link at the top right of this page to see if you may have a mail-in repair option for the region. In some regions computer owners can mail the laptop directly to Apple for a repair.
Personally I think it is unprofessional for a business not to provide a customer with details and a break down on costs.
You can always contact Apple directly to let them know how this AASP is behaving in not revealing details about the proposed repair to you and explaining why their price doesn't line up with the prices posted on the Apple website. I do know in the past Apple has taken an interest in any consumer complaints about repairs (I have no idea if they still care about these complaints). I'm not sure how people report such issues to Apple.
Keep in mind my experience is only with the US and pricing and repairs may be handled differently in other regions.