Now this powerpc.library implements a kernel running on the PowerPC CPU and provides an AmigaOS API / interface for coexistence, correct?
You can call AmigaOS API but it is not recommended due to context switches. You can not call AmigaOS API calls directly but using PPC->68k wrapper. Before calling AmigaOS API you must make sure data in 68k and PPC caches are consistent.
I would not recommend using PowerUP or WarpUP API at all.
So then the library functions eg. need to make sure that memory used by PowerPC processes are not used at the same time by 68K apps.
There is no built-in support for PowerPC. The user application is responsible for cache consistency. Using AmigaOS system structures from PowerPC code is strictly forbidden.
Now how does this library interface with the different PPC cards available?
It is handled by underlying HW drivers. Applications dont have to take care of it.
And how does this library come into play when using AmigaOS4.x or MorphOS, etc. Does this library exist in these operating systems as well in a version that maps the API calls to native stuff?
MorphOS has full compatibility to PowerUP and WarpUP API.
AmigaOS 4 only provides not fully compatible WarpUP API.
On MorphOS and AmigaOS 4 you dont have to care about cache coherency because there is no real 68k. This means PowerUP and WarpUP applications run at full speed.