What does it mean for a mode to provide a function? You say "a list of all functions exclusively available in an specific mode" and "excluding all other functions not provided by that mode".
It sounds like you are confusing a mode with the library that defines it. A library provides/defines functions. A mode generally does not do so.
If you want to get a list of all of the functions defined in a given library, then see @wvxvw's answer, for a start. You can also try matching the library prefix against function names - that is often pertinent, but it is by no means definitive.
If, however, you want to get a list of all of the functions that might be pertinent to a given mode, e.g., functions that can be used only, or are most useful, when that mode is turned on, then I'm afraid you will need to examine the library where the mode is defined. And you might even need to examine some other libraries.
A given library typically defines more than just some things that are pertinent to a given mode. And a given mode can very well make use of things that are defined in different libraries, and in some cases things that make sense only for that given mode or a set of modes that includes it.
In sum, as currently posed, your question is not very clear. You might help yourself to better answers by clarifying it.