Valid strings and arrays, \Closures, and objects with __invoke are supported.

"callable" would be the most appropriate type.

True, but it also accepts arrays representing private and non-static methods, which are not callable:

---

class Foo {
  private function bar($baz) {}
}

function test(callable $function) {}

$function = ['Foo', 'bar'];

// works as expected
echo (new \ReflectionParameter($function, 'baz'))->getName();

// Deprecated:  Non-static method Foo::bar() should not be called statically
// TypeError: Argument 1 passed to test() must be callable, array given
test($function);

---

What about callable|array then, with a note about acceptable arrays?

I would keep "callable" and say that the $function doesn't have to be accessible by the calling scope.
If not that, "mixed" and explain in the parameters section.

I'm afraid that callable is a bit misleading as it means something very precise in PHP, I'd go with mixed then.

The most important is to list exactly what types are allowed in the doc.

The documentation has been fixed.