This sounds like the "everything you create in your own time is company property since we cannot distinguish if what you do in your own time isn't company related" clause in some contracts. Under no circumstance is it actable where I live, but it can sure scare the hell out of people and presents a line of thought. Yes, some companies think they can own copyright on the things you write at home.
I always ask companies to remove that clause from contracts, I think all offers I've ever got had that clause, but also 100% removed it on request.
If my contract says that I must be available immediately at any time, do I have ANY personal time? Or is all of my time their time too?
In the US, the enforceability of that sort of thing depends on the state. Generally, if that state enforces non-competes (other than for selling the business, or managerial staff), then it most likely enforces "you're salaried, so everything you invent belongs to us".
The legal term to search is "work for hire".
I call that the "shower clause," because the company claims ownership of any ideas you come up with, in the shower.
I think, like noncompetes, there's limits to how far the company can actually enforce it, but they bank on the fact that they have lawyers on permanent retainer, and you don't. Even standing up for your rights, against blatant corporate overreach, is expensive.