Non Manifold geometry preventing loop cuts

Question

I am modelling a simple treasure chest, shown in the screenshot below. However, I am having issues with loop cuts not cutting through the whole model.

As you can see, the yellow line is the loop cut but I would expect it to follow the red line drawn on the screenshot (excuse the rough drawing).

After a Google search, I tried selecting Non Manifold geometry and this highlighted a few of my edges. I think I understand the concept of Non Manifold geometry, but I don't understand what is wrong with my model or how to get around it.

The blend file is attached.

Answer 1

Downloaded the file, here one solution:

This is only one possible solution but can be applied to both sides of the geometry, you can do other ways, but that depends on what you prefer. That said, it's important to remember that "Face Orientation", picture below lower part, helps to find the problems.

Faces shown as blue represent the outside of the volume of the geometry, red though should only be seen if you literally go between the walls. Can be seen at the end of the gif, showing "one" solution.