I think the problem is a good problem to work on. The potential benefit is huge.

The core reason to recommend Burns book over other resources is that he actually run a study to show that the book works. If you on the other hand want to create a completely new product I don't think it makes sense to copy the exercises directly.

A book is a different medium than an app and your goal is to optimise for the App medium.

The book was written 25 years ago. It feels dated.

That's before we had Martin Seligman campaigning for positive psychology. If I remember right Burns book lacks gratitude exercises.

I also consider it very helpful to locate emotions in one's own body and be aware of them on a kinesthetic level and I don't think that thought was in Burns book.

Newer CBT books might also provide good input.