She clearly states that this is a project she came up with that no one else on the team wants. If no one wants it, or is engaging with it, why would you expecting your colleagues to get excited to work on this?
There is nothing more annoying in corporate that co-workers who start trying to give you projects and tasks you didn’t want, didn’t ask for and micro-managing you horizontally.
Some of my worst job experiences came from people like this. They come up with a dumb project, then “clear it with management” then come and try to make me do it for them.
Your co-workers are not your friends, especially not if you try to start assigning them work. Because who gets the credit?
You do, not them. Suddenly they have another layer of management.
I would both avoid and add friction to anyone doing what she is trying to do in this situation. I’m not paid to help my co-workers get promoted into management or do their pet projects for them.