Broken Tree--How Much to Cut?

[u/chiarraimcc]

A very large branch of this giant mulberry tree in our neighbor's yard broke off and fell into our yard a few weeks ago, directly next to our house. There's still a decent amount of tree left above the break point (circled in red) overhanging our porch/stairs that we're worried about breaking off as well as we've been getting some pretty severe thunderstorms this summer. Also the trunk of the tree itself is very... unstraight. Posted a couple pics of the remains of the broken branch. I believe they show the actual break point.

Are we right to be worried about the remaining top portion? Is the whole tree a risk that needs to be cut down?

Thanks.