Why would physics be different in a neighboring system? Are there theories here? And if it enters our system, wouldn’t it be bound to our physics? How could you even know it was different before?

That’s something I hadn’t considered. Quite valuable understanding!

Yes, it would be very interesting if there was a material in it that hasn't been discovered yet. I imagine there are conditions out there, way out there, that bring forth conditions that aren't available here that could create new things not seen here.

This is a fascinating area. Of we do have "materials" here that came from outside of our solar system because we all contain atoms with higher atomic numbers than helium, like carbon, oxygen etc, that have been through multiple solar "cycles" that gradually make higher atomic number atoms as stars go through the ages. So you and I are both made of matter that came that way, from outside the solar system.

Of course it's different if we have rocks or some such that we could tell came directly out of the solar system, and not assembled directly here.

Well no gold was formed on earth. It all comes from stars. I'm more meaning things that would be uncommon in the universe, like perhaps being very close to a pulsar for millions of years.