This looks like a nice thing to provide. A short one/two sentence header at the start of the page to set the expectations of what kinds of questions would go on here, and how to request questions that aren't on here would not go amiss.

As for where it is located in navigation, I think I would prefer it take the place of the existing TKET FAQs section in both function and location. In theory, the manual should be a comprehensive tour through all features so the answers to these questions should be available in prose somewhere in there, whereas this fits much more easily into the API docs side of things where a user would go to try and solve a specific task rather than learning about a broad topic in the user guide. Just an opinion though, so I'm open to hearing arguments for keeping it with the manual.

I also agree that the MyST-nb code cells are slightly better aesthetically. So long as they provide the same functionality regarding the ability to test the code cells in CI (including to skip individual cells that are expensive/require device access) then I agree that getting things consistent is a good one-off task to get done at some point.