I open an Audacity project, and I want to close it without saving. Audacity closes without saving it, but in many cases it changes the project’s “Date modified”. This is quite awkward regarding my backup procedure.
Yes - that is a side effect of the new “unified” file structure in 3.x.x. The old Audacity used hundreds if not thousands of tiny little audio chunks to save its projects. The 3.x.x version uses a single “database” file to hold everything. When it is opened, is is opened in update mode. If you want to leave the Date Modified unchanged, you will have to copy the entire file, then work from that copy.
Or change the time/date back after closing Audacity (How to Change File Date or Timestamp in Windows » Winhelponline)