What is the purpose of Z-axis compensation setting in the adjustment section of the Ender 6 screen panel?
Is Z-axis compensation the same thing as Z-offset?
If Z-axis compensation is the same as Z-offset, does it change each time when you do bed levelling manually?
Does Z-axis compensation setting have any influence on the successful printing of layers after the first deposited layer? If so, how?
Generally speaking, the Z-offset is the distance between the trigger point of a Z-endstop sensor and the nozzle. But, the Z-offset can be seen as the build plate to nozzle distance, it is a modifier of the nozzle position in Z direction.
Mapping the surface of the build plate and storing the mesh to maintain a nozzle at the same distance from the build plate is considered Z-axis compensation, and is not the same as a Z-offset. These are separate things. However, the Ender 6 has 5-point assisted leveling, 4 corner and the middle of the bed. It is not capable to map the build surface as a mesh. Most probably the firmware could (as those functions are available in Marlin firmware for a long time), but the graphical LCD doesn't allow to interface with these functions of the firmware.
The Ender 6 doesn't have a Z-axis sensor (it has a Z-endstop), so automatic bed leveling is not an option and one has to do manual leveling by scanning multiple points of the build plate (as described above; 4 corners and the middle of the bed). Z-axis compensation is an offset to the level you have defined. Note the latter can be done in most slicers as well. E.g. many people like to increase the offset when printing PETG.