At minimum the hood striker on the hood is going to be bent and needs replaced / straightened. Have a close look at the hood to cowl gap to determine hood and hinge alignment.

Regardless of what you replace, the core support needs pulled back into at least rough shape as this pulls other metal you are not replacing back into shape. Making some pull plates / drilling a few holes / temp welding a pull plate to the core so pulling devices can be attached is sometimes needed.

After pulling the core, it might be back into enough shape for use. Changing a core is a larger job and should be avoided if possible as it is going to be a fender off operation on most cars.

As with painting, "welding" is 90% prep so a generic fab shop won't be interested in doing this job.

Salvage yard cores are generally cut off 6" or so rearward from the core unless otherwise specified. In your case check the area on the good car for rust then specify where the replacement should be cut to include this area.

If you get another core support you will need to plan how you are going to drill the spot welds out. If possible drill out the spot welds from the side you are not keeping on the donor car. ( This is using a spot weld cutter that looks like a small hole saw, the goal is to cut through only one thickness of metal )

On the good car you can then drill from directions that keep the new spot welds hidden.