Can the Vice President block legislation from coming to the Senate floor for a vote?

Been racking my brain about this since I've started watching CSPAN more regularly. I've come to realize after reading Article 1 Section 3 that the way Senate Republican leader Mitch McConnell seems to control when bills come up for a vote is unconstitutional. Nowhere in A1.S3 does it say the majority or minority leaders in the Senate can single handedly decide committee assignments or block laws from coming to the floor to get voted on. The VP is in fact the top officer of the Senate. The VP is the one who adjourns or convenes the Senate for voting and deciding procedures. Jefferson's Handbook also clarifies that the VP is the one the Senate defers to for all procedural or parliamentary questions. Meaning that the VP can cast tie breaking votes on any dispute in the Senate, not just legislation. With all these facts in mind would it not make sense for the VP to be the one to block bills from being put to consideration similar to how the Speaker of the House does? Or at the very least delay them the way any other Senator would filibuster? If the Senators want to move on they could just form a cloture (60 Senate votes) against the VP.

I hope there are legal experts and enthusiasts on this sub who can shed more light on this. I ask because I'm very disturbed by the amount of obstruction and corruption that goes on in Congress. The way Supreme Court confirmations have been sidelined by both parties for private gain is beyond the pale. I was raised all my life to believe this is all normal and legal. But reading our founding documents again for myself I'm angered to find out that the parties do not have ANY right to make these decisions unless the full Senate votes on it! If there's going to be one person who can block or advance these decisions unilaterally it should be the President of the Senate and/or the pro-tem. At least those people are constituonal officers. If the party leaders want that kind of power then they should be rightfully elected as VP or Pro-Tem as not too much to ask. I hope everyone can understand where I'm coming from and look forward to your responses. I also left a few links so you can cross check what I'm talking about.

Article 1 Section 3 https://www.usconstitution.net/xconst_A1Sec3.html

A Manual of Parliamentary Practice (Jefferson's Handbook) http://www.constitution.org/tj/tj-mpp.htm