Debug Library - Accessible at runtime?

https://developer.roblox.com/en-us/api-reference/lua-docs/debug
is debug available to utilize outside of studio during runtime?

I’m not too sure what you mean by this, but do you mean running code in the studio view?
If so, run something like this in the command bar:

print("thing")

You can also use ; to make a new line, e.g:

print("thing1");print("thing2")

At runtime, aka, when the server is running as a dedicated host and has been published, ie; the game players join. Does the debug library still function, ext: debug.traceback() and other methods? does those methods still retrieve data, or is that only a studio library?

Yes, the debug library is completely functional during runtime.