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Is there a keyboard shortcut for toggling or enabling "Auto fit project view to project window" (basically LMB on the 'F' button in the project window)?
If not, is there a script command I can use instead?

You can assign your own shortcut to that.

By "Is there a keyboard shortcut for toggling or enabling" I meant:
Is there an entry in the Keyboard preferences panel which toggles Auto fit project view to project window?