I will often shoot the signs as well, I keep the photo of the art and the photo of the sign together in my Lightroom Classic Library module. If you really want to store the information on the sign with the image, I believe you have to type the text on the sign into one of the metadata fields of the art photo. I suppose (but I have never tried), you could use OCR to turn the photo of the sign into text and then paste the text into the metadata field of the photo.
That's pretty much what I've done...run the image thru OCR, correct errors and paste into a metadata field. It's tedious. That's why I was hoping to be able to store the image (or a smaller jpg export) in the art image metadata.