You also need a special pan, which is probably at least as expensive.

Unless there’s something weird about that cooktop, you almost certainly don’t need new pans.

Copper doesn’t work, but cast iron, carbon steel, stainless steel all do.

Older stainless steel pans do not work. Stainless is not magnetic. Most newer stainless pans have a layer of iron sandwiched between stainless layers on the bottom of the pan. I have a set of older stainless pans I inherited from my mother and they do not work with my induction burner.

I really like cast iron cooking on an induction range.

You can easily test your pans with a fridge magnet. If it sticks it'll almost certainly work.

We switched to induction about a decade ago, had to replace one cheap skillet.

You need pans which you can stick a magnet to. Here's a set of three non-stick frying pans for US$ 30:

* https://www.amazon.com/Utopia-Kitchen-Nonstick-Frying-Pan/dp...

A twelve-piece set of non-stick pots and pans for $130:

* https://www.amazon.com/Induction-Kitchen-Cookware-Sets-Nonst...

Or a ten-piece stainless steal set for $200:

* https://www.amazon.com/Calphalon-Classic-10-Piece-Cookware-S...

Would you consider any of these "expensive"?

Plus, y’know, there’s always ReStore, Goodwill, Pawn shops, Value Village, and Senior Center thrift shops. Good pots and pans are inexpensive. Matched sets less so, but still excellent value for cost.

Most of the pans you have already bought are likely to work. I think thin copper ones are only ones not likely to work. Most other general cookware at least here support induction as well. Including the cheapish stuff.