Hi, as you can see from my profile, I have created a lot of Chrome Extensions.
After reading your project description, I went to Pipedrive website and created an account to see what needs to be done.
So, if I have understood you, you'd like that 'No Answer' button (along with its described behaviour) to be attached to dialog window that appears when clicked on "New activity'?
You mention this: "A new popup will appear, and some details need setting."
But no new popup appeared after I clicked Save?
Regarding details on my solution for your project, it's the usual way to handle things like this, a combination of content and background scripts makes this possible.
Let me know if I got you right, and also answer me please about that "new popup" thing, because it doesn't appear to me after clicking Save.
Regards, Stefan