Tested with Only BYG, but am currently playing on ATM6-1.5.3b, Forge 1.16.5.36.0.43 (also 46), with BYG byg-1.1.10,

Dunes, Babboas, Mohave and Jacaranda Forests, The Black Forest, and many others have solid chunk borders in the majority of places, provided the chunk contains a BYG biome. This does not seem to affect anything above 63, but it does affect the majority of space under the surface. It looks like the carving may be happening before BYG has generated the biomes.

Mineshafts are fine, and are not cut off, vanilla mineshafts and YUNGs still generate, same goes for Quark Caverns, they generate just fine as well. It does cut off regular winding caves, underground lava and water pools, on land, in oceans, etc., and ravines, both on the X and Y accesses..

Now, there are carvers that do make their way through, very rarely, but I believe they are modded carvers, or carvers that BYG may be adding to account for this happening. In one of the images below, you can see a ravine that literally cuts off, but then starts back up again mid way through a BYG biome chunk.

Of the following images, the first set are from ATM6-1.5.3b, Forge 1.16.5.36.0.43, the second set are from only BYG with Forge 1.16.5.36.0.46.

ATM6:

BYG Only: