Usually (close to) universal answer is something like is: "If you've used any employing entity resources, even incidentally, your employing entity owns it, especially if the project is directly related to the business"

Some places will attempt to assert more ownership and some will not.

They pretend to, as would many companies if asked. I don't know how that would hold in court though. They also, for instance, pretend it's illegal to discuss your salary while the opposite seams to be true, so...