This is most likely a position sensor issue related to the gear lever not reporting to the cluster, which is why it effects different models and drivetrains the same way. It's also why Lincolns weren't effected because they used buttons, and Ford would later redesign everything with those infamous dials. This is hilarious when you remember that the lever is just an elaborate button in a solid state system that mimics the old mechanical linkages people are use to. It's not really a huge safety issue as long as you pay attention to the lever's position instead of the dash readout, but obviously it needs to be fixed. I can't imagine the sensor is expensive to replace, but cracking into a console isn't the quickest thing to do.
The other thing the Lincolns had which also eliminates this concern is auto-park, the transmissions would automatically shift into park to prevent rollaways. This came to all Fords with the dials and 2021 F-150 with the motorized lever (it's actually the reason the folding motorized lever is standard, it's a safety system). Technically you could still implement the Auto-Park feature with a mechanical lever, but you have to instruct the driver to move the gear lever back to park to reset the system which is why Ford may have chosen not to go this route (others have).
This is why I've always loved the solid state gear selectors, they are an essential safety innovation. And this fiasco now just further illustrates why.