There is carbonized deposits on both the stove and stockpot that seem impervious to hot water and vinegar.
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Sam is a trusted home cook.
For the pot put in at least 1/2 inch of HP and add tsp of baking soda.
Heat it...it must be heated. to start the catalytic reaction.
It will stink, harmlessly, but turn on vent.
Scrub with a scouring 'green back' sponge..and repeat.
It's magic the HP will lift off the carbon from pot. It won't remove stains..but will get rid of crusts..chemically bonded to the pot.
let it boil a bit..the HP will bind to the sugars bonded to the pan and lift off the carbon.
The peroxide loves to bind with carbon..sugars. and releases it bound to surfaces.
For the stove I really do not know..but heating up a HP mix and let that bubble a bit...this will depend on your stove. I"ve done it on a glass top stove heating pouring to lift off high carbon (sugar) crusts..and it worked great.
If you have a bottle...try it and report back. I'd like to see if this works for you for your pot.
I find that barkeep's friend works really well. I've also done the baking soda trick, boiling it as Sam notes above. Never thought to add HP, will try that next time.
Another vote for Barkeeper's Friend.