From an NPR article:

Why don't the Senate leaders stop him?

The current Senate Majority Leader Chuck Schumer has made it clear he considers Tuberville's blockade an abuse and an outrage. The GOP's McConnell has also said he does not support the "blanket hold" on military nominations. Both have acknowledged the pleas coming from the Pentagon and from the ranks, and they have done what they could to encourage Tuberville to stand down.

But the leaders cannot simply bulldoze the senator from Alabama. Their power is restrained by Senate rules and traditions and by the sentiments of their respective caucuses.

If the issue here were an ordinary piece of legislation, the leaders would seek a unanimous consent agreement that would bring that matter to the floor. Individual senators may object to that with a notice that they seek "extended debate" on that legislation. This is an implicit threat to filibuster, and the majority leader routinely files a cloture petition and holds a vote.

If cloture fails, the legislation does not go to the floor. If three-fifths of the Senate supports cloture, the legislation can be brought to the floor with time limits on debate.

Presidential nominations have been largely exempt from this since 2013 when a Democratic Senate majority decided only nominations to the Supreme Court would be subject to filibusters. In 2017, a Republican majority decided to extend that exemption to include Supreme Court nominations.

Nonetheless, Tuberville's maneuver has the effect of freezing confirmations for the current backlog presidential nominations because they are submitted in batches for group consideration and approval. The batching procedure itself requires unanimous consent, allowing even one senator to stand in the way.

The Senate majority leader could bring the nominations to the floor one by one for consideration by regular procedure, but that would require two to three days for each. Had the Senate tried to individually process even the first 150 promotions Tuberville blocked back in February, it could have done little else in the months since – and it would still be far behind on confirmations. That is scarcely practical when the military alone submits hundreds a year and the larger executive branch far more.

Moreover, just as the Pentagon bristles at having a single senator dictate its personnel policy, so the Senate leaders are loath to have individual senators deciding when and if the Senate can proceed with normal business using its usual procedures – such as the batching of nominations.