The VP does not legislate, or approve legislation.

The VP is literally the head of the senate and can vote on senate bills to break a tie

And you are also claiming that the VP has no executive power whatsoever. You also seem to assume that she has no power to legislate indirectly, by collaborating with legislators, despite holding the second most powerful executive position in the USian government.

Can you, in your own words, explain the difference between the executive and legislative branches of government?