SdFat: How to go to parent directory?

There is not a supported way.

I wrote a function:

  /** experimental don't use */
  bool openParent(SdBaseFile* dir);

I made it private since I was not to happy with the design. No one asked for it so I didn't follow up.

You could edit SdBaseFile.h at about line 358 and make it public. I may not work since I wrote it a long time ago.