What is a good method to clean stainless steel hot water pot?

Wow! That is quite a patina you have built up there.

I would try Barkeeper's Friend (oxalic acid) in a thick slurry and soak it for a day and see what happens to remove the blackening. It still won't remove the orange enamel paint though. So you might end up having to wet sand it after taking it to a wire wheel.

Sound like a project.

if it is just the outside wall of the kettle that needs to be cleaned (of what looks like grease) than any scouring pad or course steel wool should work. To expedite the task use a cleaning powder like Ajax or Comet. Rinse well under cold water.

If you also want to strip the colored tinting off follow the above steps and then use wet/dry 120 grit sandpaper.

I suppose there might be some paint there, but it certainly looks a lot like burned-on grease/oil. Have you got a larger pot or washtub (perhaps sink) this can fit in? Even a plastic bag might work.

First thing I'd try would be HOT water and baking soda (sodium bicarbonate) and let it soak overnight. That cures many of my nastier stained stainless problems simply.

If not enough, I'd then go the opposite direction and use an acid (barkeepers friend was already mentioned, or citric acid, or vinegar, also with an overnight soaking.)

If both of those fail then I'd start contemplating paint strippers, though I might first switch back to (stronger) bases and try the already mentioned oven cleaner first. Be very careful with the stronger chemicals - a new pot is far less trouble and expense than a chemical burn on you.

Have you ever made or even heated tomato sauce and has some drip down the side and leave a super shiny streak down the side of your pot after cleaning it off? That's because it's a great cleaner for stainless and for copper as well. Open a can of tomato sauce and soak the stainless in that for a little while, it'll soften up that patina so you can get to the shiny metal without damaging it.

If this is really stainless steel, all parts of it, EZ-off oven cleaner should be ok for it. I have used it to get the jellied oil off of stainless steel items, with good success. Spray it on, and let it sit a few minutes, approx 2-10 maybe, then wipe it off. One of my pots had grease cooked on for decades, and it needed multiple treatments,but it was obvious from the very beginning that it was working. It did not damage the stainless steel underneath. But: if any part of your item is some other material, I wouldn't attempt it.