J-B Weld 8267 SteelStik Steel Reinforced Epoxy Putty Stick - 2 oz.

You are looking for epoxy putty. It comes in small rolls or sometimes sheets like you motioned. It should be under $10 at most hardware stores. https://a.co/d/0dyOyCGB

Yeah, I think that's a good idea. I know metal filler products do exist too, although I've never used them. Something like this would work, I should think.