I’m a drone newbie.  I live in a mountainous part of the US.  I’ve been setting up waypoint flights for my Mavic 3 using the DJI maps but cross referencing to Gaia topos for accurate elevations.  

I’m hoping someone can explain how the drone figures height above ground.  For example when I fly it over the edge of a cliff it maintains the same altitude even though distance to ground is now several hundred feet lower.  Yet when it returns to home on the cliff it achieves the preset RTH altitude above the height of the cliff.  Is this all GPS or does the drone “memorize” map contours as well?

The drone only knows its altitude relative to where you took off.  If you fly off a cliff it will report the same height which will be wrong.  

As @DAFlys points out, the drone height displayed on your RC is always relative to the take-off point, regardless of what terrain it flies over.
If you want to pre-program the drone to fly a mission whilst remaining at a constant height (say, 50 metres) relative to the terrain over which it flies, the programming needs set each waypoint as Relative-to-Ground. This can be done with certain third-party Apps. Whether this can be achieved with DJI Fly or DJI Go4 Apps,  I've never had occasion to find out. Have a look in the manual, or wait for one of the more experienced forum members to comment.
If you want to investigate further, one such app is Litchi. And there's a very good tutorial video from a satisfied user here:

Blériot53 Posted at 4-26 10:49
As @DAFlys points out, the drone height displayed on your RC is always relative to the take-off point, regardless of what terrain it flies over.
If you want to pre-program the drone to fly a mission whilst remaining at a constant height (say, 50 metres) relative to the terrain over which it flies, the programming needs set each waypoint as Relative-to-Ground. This can be done with certain third-party Apps. Whether this can be achieved with DJI Fly or DJI Go4 Apps,  I've never had occasion to find out. Have a look in the manual, or wait for one of the more experienced forum members to comment.
If you want to investigate further, one such app is Litchi. And there's a very good tutorial video from a satisfied user here:

I watched the Litchi "Fly Relative to Ground" youtube vid and then checked out the app, but it says its not compatible with Mavic 3 because "DJI has not released a developer SDK" for the Mavic 3.  This quote is over my head, but I assume it means the method demo'd in that youtube video can't be used with Mavic 3?  

Zanetia59 Posted at 4-26 12:29
I watched the Litchi "Fly Relative to Ground" youtube vid and then checked out the app, but it says its not compatible with Mavic 3 because "DJI has not released a developer SDK" for the Mavic 3.  This quote is over my head, but I assume it means the method demo'd in that youtube video can't be used with Mavic 3?

Ah yes. DJI usually only release the SDK (Software Development Kit, if memory serves)  quite some time after the release of each new drone model. So it will be a while until Litchi can include the Mavic 3 in their range of devices catered for.  I have a Mavic 2 Zoom, so I can use Litchi for waypoint missions, and do so fairly frequently.   I hope someone else pops up to help you out