I thought I'd check with the rest of you even though I think I know the answer.

Here's the background - something got burned in one of my stainless steel pots (not me) and I wasn't happy with the result after cleaning it with ajax and the regular plastic scrubbing pad.

It's steel, so I decided to just do the obvious and cleaned it with a real abrasive pad that removes metal. So far so good, got nice new shiny steel surface.
I know from honing and restoring razors that steel is quite reactive and oxidizes easily but I thought I'd go for the trial and error and decided to just start cooking instead of waiting a couple of weeks for the surface to become a bit less reactive. I figured in the worst case food will stick badly and I may have to scrub it again.

Well that's exactly what happened - I boiled some milk and ended up with a uniform layer of brown at the bottom (already scrubbed back to fresh steel).

So I think I need to season the fresh steel surface and make it less reactive. I'd imagine that high-temperature smoking point fat would work just like it does for cast iron, but thought I'd post and ask. I don't think it needs extensive seasoning like cast iron with several iterations, probably just a basic heat up and cool down would suffice.
I think it's clad with a copper middle so the conductivity would be pretty good and the stovetop would be fine.

What do you say?