So I dug out a full cup of gravel and silt, along with a small foam ball, a penny, and a nail.
After flushing it with water to make sure it was good and clean, it flows great.
It had a threaded plug to block the cleanout, but it wasn't the right size, and besides the threads in the cast iron are all rusted away. So I filled it with a compression plug. Seems to be working well.
Before:
My plumber friend actually suggested just hiring someone you know and trust who knows what to look for to check out your short list, rather than an official inspector. Official inspectors are very official, I guess, and not necessarily super knowledgeable about the often-missed things that are frequently problematic. I don’t know if I’m explaining it well, but his logic was sound when we were discussing it. He's a guy who bought an old farmhouse, tore it down to the studs, and rebuilt it. He's got some knowledge.