What it is, fundamentally, is information that propagates into functions,

Actually, it's information that propagates into terms. Which can be function calls, but in Perl5, you probably can see the most number of different possible contexts when the value of an object needs to be fetched: overload dispatch (boolean context, string context, numeric context, scalar deref context, array deref context, hash deref context, code deref context, typeglob deref context, iterator context). And beside the mentioned list/scalar/void context, Perl also has lvalue context.

Note that not all contexts are mutually exclusive.