IIRC my high school education, the SENATE does not initiate a budget, period. At least technically. In the past, while the President or the Senate may propose and/or pass something, it still has to go to the House where they are the only entity responsible and lawfully allowed to pass a fiscal budget. All money-based bills have to be passed by the House, period.
What happens in practice, though is that Democrat Houses accede to the Senate and rubber stamp their budgets. The fact that Democrats don’t control the House now is where the disconnect is.
Reid is not technically required to submit or pass a budget; that is the purview of the House of Representatives.
You are technically, and literally correct. It’s worthy of note the House has passed a budget every year and dutifully sent it to the Senate. It’s not that the Senate didn’t make a budget, it’s that they never brought the ones they were sent up for a vote.