How to use frozen patties in recipes asking for ground beef like chili, meat sauce, and meatballs?

If the patties are just ground beef, then use them the same way you'd use any other ground beef; pull it apart with your hands or break it up with a spoon or spatula in the pot.

It may be that your burgers include other ingredients for flavour, in which case those other ingredients will also be in whatever you make, but they shouldn't significantly affect the cooking.

Some burger patties could include things like egg or breadcrumbs for binding and to bulk up the mixture, but it doesn't sound like that's the case from your description. If that is the case, then they will still work fine for things like meatballs but might make something like chilli have an odd texture.