osgEarth composites layers by rendering them one on top of the other with an LEQUAL depth function, which prevents z-fighting. So that's not the issue. It could be related to your driver upgrade. Is this osgearth_toc, or your own app? Are you doing anything custom with the near/far planes?
I had applied remoe's git pull request 'GEOS 3.8 compile fix #1497' so that I could use the stock geos (3.8) on Ubuntu 20.04.
However I ran into problems with using a osgEarth::Util::Controls::Frame(). In that my application was crashing.
I dug deeper and found that objects created in geos were losing thier contents so that a subseqent call later would crash attempting to access the coordinates. I've spent most of today and half of yesterday trying to find out when the contents disappear but I'm not having much luck.
I've a hard timescale so I've abandoned the debugging for now... so I built geos 3.7.3, rebuilt gdal 2.x, osg, osgEarth 2.10.
Runing with the new builds the problem with the z-buffer has gone away and the Frame object draws.
Nothing else has changed in my build other than the version of geos. Neither has any of the graphics drivers or other dependencies.