What is the “home remedy” for making a metal baking pan shiny ?

If you grow, or know else someone who does, rhubarb leaves work great. Oxalic acid is what makes rhubarb tart, is the same active ingredient in brasso and barkeepers friend. Alternatively, barkeepers friend is my favorite for cleaning pots and pans. I have a stainless steel set that I've had for about ten years, they still look brand new thanks to this stuff. And I cook everyday

Baking soda, make a paste, leave over nite. Scrub in morning. Like new!

try putting water in and a couple of dryer sheets, let sit over night.

If you're looking for a more natural, chemical free approach, I find this method super efficient! https://theseamanmom.com/natural-way-to-clean-pans-and-pots/ I've been using it for all my pans and pots for years and I couldn't be happier with the results. I even apply it to clean my stove top.