I'm wondering if static parameter functions created in Swift can't be used in ObjectC.

xcode version is 15.1 (15C65)

Yes, this should work:

@objc class MyClass: NSObject {
    @objc static func foo(_ param: Int) {}
    @objc static func bar(param: Int) {}
}
void test(void) {
    [MyClass foo:42];          // ✅
    [MyClass barWithParam:24]; // ✅
}

The obj-c name could be customised if needed if you don't like the name made by default.