The slowing down is a function of conductivity. Electromagnetism means the magnet induces current resulting in magnetism pushing back. Ferromagnetism on the other hand is a somewhat rare property of some metals where all of their atoms can be pushed into the same magnetic orientation.

Disclaimer I'm an engineer half remembering this stuff

Doesn’t whatever is in the windings have to have some magnetic interactivity too?

Nope! The coil windings don't need to have any intrinsic magnetic properties at all. A magnetic field moving over any conductor will induce electric current. Doesn't even actually need to be made of metal. You could technically do it with anything conductive -- say, a hose full of salt water.

In fact, a lot of modern generators/motors don't have any magnetic parts inside them. Instead of rotating a permanent magnet, you can rotate an electromagnet, which is just more copper coils with a current passed through them. And that can work as your magnet to create electricity with. That approach, though, requires some startup power to energize the electromagnet, so it's not really suitable when you're trying to bootstrap the very first production of electricity.

Or does it not matter because the conductors are making an electromagnetic field and the base magnetic properties of the windings don’t matter as long as they conduct? (is how much they interact with magnetic fields related at all to how good of a conductor the material is?

Yes to all of those. To put it in a (perhaps overly) simplified way: Electrons in any and every material are 'grabbed' by magnetic fields. When the magnetic field moves (relative to the material the electrons are in), the electrons want to move with the field. (Each electron is, itself, a tiny electromagnet.) The more conductive the material is, the more easily the electrons will be able to move along with that magnetic field. And moving electrons is what we call 'electricity'. In a poorly conductive or non-conductive material, the electrons can't move easily -- they stay stuck where they are in the material and electricity doesn't flow well.

(Electrons flow well in metals because the way metal atoms bond together with each other causes them to share outer shell electrons with each other. In a solid piece of metal, all the atoms are sharing some of their electrons with each other, leaving the electrons freely able to hop around from atom to atom anywhere through the material. Fun fact: this is also why most metals are reflective and shiny (when not oxidized/corroded) -- incoming photons of light hit this swarm of freely moving electrons and get bounced right back out.)

Are you an Electrical Engineer or some type of materials scientist that can answer all of my random questions?

Science fiction writer, mainly, lol! But it does mean I spend a lot of time getting into the weeds of how such things work.

Did actually take one semester of engineering classes once, before deciding to go a different direction.