According to this account, the power of the Senate Majority Leader is a matter of tradition in the US Senate, and so the president of the Senate (the Vice President of the US) can simply recognize some other member of the body to bring a motion to the floor.  (A quick Google finds similar arguments here.)

This is intriguing, but I do not think that this is particularly realistic.

Joe Biden pines for the “good old days” of the Senate, and I don’t think that Kamala Harris would be particularly interested in presiding over the Petri Dish for narcissistic sociopaths that is the US Senate 4 days a week, but it would be useful to raise this possibility on the down low, and when questioned, issue a non-denial denial, to move things along.

This would be analogous to what happened during various showdowns about the US debt limit, the Obama administration denied that it was going to use seigniorage (the platinum coin of arbitrary value) to make an end run around Republican demands, but it does appear that the buzz around the concept did moderate reactionary intransigence:

Even if the Democrats don’t win control of the Senate, there is a wayto strip Mitch McConnell of his power for good: priority recognition.

According to Article I, Section 3, Clause 4 of the Constitution, the Vice President is also the President of the Senate. The Majority Leader is not a position that exists anywhere in the Constitution. The reason that the Majority Leader has near-dictatorial powers to control floor votes is because of a tradition that dates back to 1937. The tradition is that the Vice President gives the floor leaders priority recognition. Most notably, this is not a rule in the Senate.

As President of the Senate, Vice President Harris could give any senator priority recognition. That senator could then decide on all legislation that is brought before the entire Senate. Even with a minority in the Senate, Vice President Harris could simply give Chuck Schumer priority recognition. He could decide what is voted on and what isn’t.

This would change everything. Without Mitch McConnell to hide behind, the moderate Republican Senators would be forced to vote down every Cabinet member, bill, resolution, everything that Harris would want done. Without McConnell, anything even remotely popular with at least two [Republican] senators would pass. Including getting a cabinet assembled.

Given that Mitch McConnell is indicating that he will be even more obstructionist and intransigent about Biden than he was about Obama, the threat of this sort of action needs to be on the table as a subtext at the very least.