A Microsoft file hosting and synchronization service.
The error shown in your screenshot suggests that the desktop application is having trouble opening the notebook's cloud location, although this doesn't necessarily indicate an actual permissions problem since you can access and edit the notebooks online. Could you please confirm whether all your notebooks are affected or only specific ones? Also, are you using a personal Microsoft account or a work/school account? Finally, does the same error appear when opening a notebook directly from within the desktop application rather than using the Edit in Desktop App option in your browser?
As an additional troubleshooting step, please open the OneNote desktop application and navigate to File > Open > Open from OneDrive, then check whether your existing notebooks appear in the list. If they do, try opening one directly from there instead of using the browser link.
If the notebooks don't appear or the same error occurs, please try creating a small test notebook in OneNote for the web and check whether the desktop application can open it.