The Kansai Wide area pass that I'm talking about doesn't include access to museums. But some of the smaller passes (like the one of Osaka that you mentioned) do. Those passes don't include Shinkansen, though.
From what I see[1], that is an umbrella term that encompasses a few passes, including the Wide Pass. Maybe some do include attractions; I didn't know that!
I also looked up Tohoku JR passes for an upcoming trip and it wasn't affordable at all. I'm better served using single tickets even when riding the Shinkansen.