I have written a python script to 'de-booklet' a PDF. Sadly, Apple have now removed python from macOS (since Monterey 12.3), which now makes handing people useful scripts on macOS much more difficult.
Prior to Monterey 12.3, you could just run this script in the Terminal, with the filepath of your PDF as an argument:
You could also put it in an Automator or Shortcuts.app workflow, using the 'Run Shell Script' action.
But now you'll have to install python3 and the pyobjc library, and use a newer python3 script:
I recommend installing python3 directly from python.org:
Once you've done that, in the Terminal, type
pip3 install pyobjc and press Return.
If you want to run it as a Quick Action in the Finder, or from the Services menu, then see the options selected in this image from Shortcuts.app.