I'm also worried that CS1->Zero may not be optimal. I asked this back in the summer but it seems like people couldn't come to a conclusion, some people said CS spoils Crossbell, others said the opposite. Seems like you can't win.
Zero is barely acknowledged in CS1 in a single newspaper issue that says very little. It's Ao/Azure that references events from Cold Steel and Cold Steel 1 and 2 reference moments from Ao/Azure.
In terms of how spoilery it gets, well, it depends. Zero and Ao released first, so the notion that both spoil each other that you see so often mentioned is faulty to begin with as every element referenced in Ao that pertains to Cold Steel is knowledge that you are supposed to have. But considering how most of us played CS 1 and 2 without Crossbell, it's understandable that some people have fondness for some twists and turns that weren't really twists and turns if you've played Crossbell before.
I think Ao/Azure spoils significantly less than CS1 and 2 do, as only two text crawls and one conversation (from memory, might be slightly off) deal with Cold Steel events, but it does reveal what the conflict is and the result of said conflict, which is why the opinion that both spoil each other is so widespread, but CS1 and 2 are far more liberal about it directly showing events happening in Crossbell, and revealing villains as well as the final dungeon itself. While context is often missing, you get a fairly decent mapping of how Ao unfolds event wise, even if the details are kept from being addressed for the most part.
To put it simply, Ao teases Cold Steel, Cold Steel references Ao. Both arcs make the player aware of certain things happening in the plot of the other arc, that's unavoidable. Which option is better, is, for better or worse, different for everyone. I prefered not knowing things I should know playing Cold Steel first, and regretted knowing certain things having played Cold Steel first. You win some and lose some regardless in my opinion.