Want did “ takings a break “ mean in a relationship mean

It can mean something different to each person so you really need to agree on what your definition is. For some people taking a break means they're not seeing each other or talking but they're still in an exclusive relationship and not talking to anyone else. For others taking a break means temporarily broken up and you're allowed to date others during the break, but you expect to get back together or at least revisit the idea of being together.

Depends on the terms set by the people in that relationship. You’re not on a break though, you’ve clearly stated you broke things off. He chose his family over you. Don’t let him manipulate you. If you can’t go no contact you need to delete and block him for your own wellbeing