I checked more. It is a problem with the Windows Defender controlled folder access feature.
It happens for at least for 1.23.3, 12.4.0 and 1.25.0-beta0. The beta in portable mode. In portable mode, I get notifications that defender is blocking folder access, for the others I do not, but saving fails with the error messages shown by @Jinstarro.
To get things working I can turn off controlled folder access (which I do not want ot do) or explicitely allow atom through, see screen shot. I did not fully appreciate yesterday that it is not sufficient to just allow atom.exe in the default location (C:\Users\myUser\AppData\Local\atom), but that I also had to allow atom.exe in the corresponding app-version-nr sub-folder. This seems fine for now, however, I will have to remember to allow the new executables through after each upgrade, which seems inconvenient (update.exe also needs to be added). Is there a way to get atom whitelisted by Microsoft? As I mentioned Notepad++ does not have the same issues.