how pitted is the inside might be better to order a replacement barrel 10/22 barrels are really easy to change and are usually 40-300$ depending on quality of replacement parts. the other option would just be replace the entire thing 10/22 usually goes on sale in spring at Cabela's and you can buy a stainless one for 250-300$.
I refinished an old cooey barrel. Sandpaper of reducing grits. Steel wool. Got it down to the bare steel and tgen that semi ok cold blue stuff.... a few coats. More 00 steel wool for some shine then oil and it looked pretty good.
Soak it in sea foam “deep creep “ overnight than hit it with 0000 fine steel wool
I'll try that. It's a trapping rifle so aesthetics is not important. I've seen those so-called stainless barrels and they don't look very stainless to me. More like silver spray paint. Anyway, just cleaning this barrel will be fine.
I have used electrolysis in the past. Worked awesome if you want to give it a try. Washing soda, some rebar, water and a low rate battery charger is the tools required.