Hi! I have an old coal door in my kitchen.

Is ir something like this first picture? Do you feel cold air from down below when you walk past it or open it?

Since you don't like it, why not remove it? I'm not familiar with its construction, but look around for screws and nails. Perhaps you can see the door from underneath? For sure they didn't have construction glue, but i wouldn't put it past 'em to use tar to seal it up. Once it's out, seal up the wall as Bob Vila recommended for a large drywall hole:

https://www.bobvila.com/articles/how-to-fix-drywall/

Also, once it's out, throw it in a metal pan of paint remover. Because it's an antique and part of you home's history, don't throw it in away, please. If you know an antique dealer, they'd be happy to take it off your hands. See the screenshot from Etsy. $60 I could use; however, l hope you'll turn it into something else useful for your home.

I don't know what the back looks like, but I'm sure you could use it in your home. You could use it as a hot landing spot by the stove. You could build a thick wooden tray for it, slip the metal portion into the oven or on a low burner and warm it as dinner is getting ready. Then put the hot door into the tray, put the casserole on the door, and serve a dinner that will stay warm through seconds and coffee afterwards. I'm inagining you'll have to use something like a dremel to build a board that matches its dips and peaks. Or, give it a wooden base and backing and tilt it up it for a door stopper or a bookend.

One last thought. Since it's part of your home's history, record that on it. "This house, at 123 Sesame St, was built in 1903. This is its original coal door."

I once looked at an old house for sale where the original owner had scribbled in pencil in the master closet: when it was built, and more important to him, I'm sure, how much each portion, barn, chicken coop, house, lumber, roofing, piping, had cost! What a treasure!