Is it safe to have multiple overlapping

pulumi up

or

pulumi down

commands running in the same directory if they're on different stacks? I thought/hoped so, but then I think I saw it get confused once.

Yes you can. I do this all the time in CI. I'm using a self managed backend but i imagine it's the same for cloud

Confirmed, stacks have independent state. If you see an issue with this, please file a bug report. The Pulumi Service ensures only one deployment (up, down, refresh) runs concurrently on the stack level.