Tooki is correct....
Soldering iron tips were all copper or something close to copper initially. Then someone put a protective iron coat on them to prevent corrosion since the small tips would corrode and destroy themselves. I think Ungar was one of the first to use iron coated tips.
You can make soldering tips out of good copper wire (for old fashioned electric soldering irons), I have and they do not last very long but you can fix them with a file.... I have used brass rod and it works OK. Still corrodes rapidly.
The further "stainless" coating is there to keep the solder from running up the tip and keep it on the only Iron plated tip. This is a further "improvement". It is very hard to solder stainless, ever try? Stainless tools like old dental picks do not stick to solder hardly at all. The Nickle plating is there to accept the stainless plating. When plating steel or iron first a Copper plate then a Nickle plate and finally a Chrome plate was used. Chrome Bumpers..
I do not think solder sticks to Nickle very well either....The nice shiny coating you see on stainless steel is actually an "Oxide" that forms on the surface, Same thing happens with just Nickle or Chrome. Solder does not stick to this normal coating that forms in the air spontaneously.
I once replicated old Nickle plated screws on an antique vehicle, we used stainless screws and polished them on a wheel very well, after a few days you could not tell the stainless screws from the original Nickle plated screws.
Stainless Steel has Nickle and Chrome in it.
The suggestions to "Treat" the area that is not supposed to accept solder probably do work for a while but the problem is that the "Stainless Coating" is no good.
I use Aluminum based anti Seize Lubricant on old soldering parts that I do not want to accept solder or parts I do not want to corrode and get stuck. Like the inside of solder suckers and solder sucker tips. And the base of solder tips. You can buy this at an Auto supply store. It is made for exhaust manifold bolts (also used on jet engine parts). It is kind of a gel and with heat from the soldering iron apparently forms an Aluminum coat on the part being treated.
Perhaps try this?
You can apply it to the cold part and then heat it up in the handpiece.
It smokes quite a bit for a short time, open a window.
I think there are Copper based anti seize and Aluminum based anti seize "lubricants" I don't think the copper based ones would be helpful here.
The coating is kinda like an Aluminum "powder coat".