So I picked up my car yesterday with new heater core replaced. Battery was indeed dead, and had to jump start it in the lot to get me on my way. But I think the dealership left a light or something on inside the cabin for a week, and ran the battery completely dead, and of course they'd have to keep jump-starting it if they never recharged it or drove it for any meaningful amount of time to allow the battery to recharge. So after getting home yesterday I hooked it up to my battery smart charger at home and charged to 100% and the car started fine this morning. So we'll see if I really need a new battery.
As to the heater core, the "service sales advisor" said verbally they did a coolant flush and replaced heater core and also "some gasket". The service tech write up on the invoice explained the DTC and diagnosis and repair, and he just indicated he drained coolant, replaced heater core, and performed vaccuum fill to refill coolant and ran engine to operating temperature and all heat functions work properly. So it's not totally clear to me if they really did a flush. The TSB for the P2457 DTC says they are supposed to run a full coolant flush twice before replacing the heater core and refilling with coolant a third time, using 3 gallons of coolant mix. But no mention that they did this, and the invoice just indicates 1 gallon of coolant.
Also, the coolant refill was G12 Evo (G-12E-100-1G-CON). So this is the glycerin based version of G12 that replaces G13? Isn't it the glycerin in G13 that is thought to be causing the clogging of heater cores? Also, what can be safely mixed with G12 Evo? I have G13 concentrate and about a half gallon of plain G12 50/50 mix on my garage shelf. I don't know why VAG had to make it so confusing with 4 different versions of G12 and also G13, some of which are compatible with each other and some aren't. The nomenclature sucks and is needlessly confusing.
Last point, I also noted in the invoice that the part number of the heater core now ends with suffix "C" so perhaps there has been some revision or improvement to these heater cores. The older TSB and prior comments mentioned the part number ending in "B".
Let us know how it goes. Hope they get it done quickly.