I did look at your post and everything looked normal to me for an older stove.
The brown residue just looked like smoke residue that was able to get out of the oven cavity around the light socket.
But you said that you smelled burning plastic so without actually being there to inspect the wires I was not 100% sure and I did not want to be responsible for a house fire if I was wrong.

Sounds like you found the source of the smell was actually the terminal block.

If the line cord has any signs of it's wires overheating I would not reuse it.
Also if the cord wires are good then be sure to clean the connectors with some fine sandpaper or emery cloth before using it.

The problem could have been a loose connection at the terminal block or a bad crimp of the connector onto the line cord wire. When electricity passes through this connection, it sees this as a resistance and produces heat. This then degrades the connection causing more heat and so on and so on until the connection fails.

I have a Whirlpool Gold convection electric smooth top oven (GR673LXSS1) and noticed a burning plastic smell the last few times we used the oven. I pull the oven and the panels on the back and found some burn residue areas coming from the light socket area that had started singing wires above it.







The burned/singed areas are still intact and not too bad honestly. I'm wondering if I can replace the whole light socket assembly and have any confidence that that might actually fix the problem. When I pulled it out to look at it more I noticed there was not a lot of insulation right up close to it, but about 1/8 to 1/4 inch back from the edges of the light assembly.

Any thoughts on if this might actually be fixed by replacing the socket and somehow getting more insulation to provide a tighter fit.

thank you for any help