@SIGINTMy question is: Does a thread GM need to be staff, or can we, as players, create and run missions for other players?
Yes you can. No you don't need approval from staff unless you intend for their to be rewards that are beyond the scope of what is already allowed.
I had a conversation with Circ regarding this in the Discord chat, and I wasn't super clear on what the response was, but the way I ended up reading it was, "If an NPC has any capability/intention of affecting a PC, in any context, they must be submitted and approved as a PC themselves".
I think your reading on that was a little too strict. Note that I'm playing an NPC that is setting up the relationship between the Ragnarov Fleet and the UFP without creating a character profile. The NPC is influencing the relationship of the characters, but I don't need a profile because it doesn't have any special abilities or even a name or enough stuff around it to merit being approved.
Hopefully that answers your questions.