text: Title: Notebooks with only markdown cell edits don't get republished
  Body: ### Describe the bug
  
  Using `jupyter-cache`, if I edit only markdown cells in a notebook, the notebook is not re-executed (which is fine), but nor is the target HTML document updated with the edited markdown content. 
  
  ### Reproduce the bug
  
  Edit just the markdown cells in a notebook and then rebuild with `jupyter book build .`. The content is not updated in the final Jupyter Book.
  
  ### List your environment
  
  jupyter book --version
  Jupyter Book      : 0.12.2
  External ToC      : 0.2.3
  MyST-Parser       : 0.15.2
  MyST-NB           : 0.13.2
  Sphinx Book Theme : 0.1.5
  Jupyter-Cache     : 0.4.3
  NbClient          : 0.5.1