I am looking to edit a project in which currently all the question slides have plain grey backgrounds. There is nothing under the properties panel and all of the buttons to insert text, shapes, media, etc are greyed out/un-clickable.
I looked through the slide templates that are in this project and none of them look like the question slides where it is just the questions overlayed on a plain grey background.
I suspect you are talking about the quizzing master slides? Each theme needs to have 5 master slides related to quizzes, and that is the case both for non-responsive and responsive projects.
If I am wrong and you are pointing to the Quick Start Projects, where some also have quiz slides, I have to disappoint you because some of them have dedicated quizzing master slides, but some themes are 'incomplete' to say it nicely. The quiz slides in that last case have been created as standalone slides. That is a pity because it is not possible to have a score slide in the same style if the theme has not been updated.
Due to my hesitation about what your problem really is, please post some screenshots and tell me if you talk about master slides or the Quick Start Projects. It is also important to know the type of project: responsive or not? The themes are different. Here is a link to a blog post I wrote about the quiz master slides for a responsive project with Fluid Boxes:
If you only want to have another background for the quiz slides, you just have to change the background of the quizzing master slides. Maybe your master slides are using the project background and that is a solid grey color?