decltype(a) is int. This corresponds to invoking f with an int prvalue — something like f(7). That one indeed doesn’t compile, because a non-const lvalue reference cannot bind to a prvalue.
What you’re doing instead in main is calling f with an lvalue, a, to which the reference can bind just fine.
To get the correct result from std::is_invocable, use the expression form of decltype by adding parentheses:
std::is_invocable_v<decltype(foo), decltype((a))>
// ^ ^