Recess Appointments of Military Officers

A story in the news is that Senate Tuberville (R-AL) is holding up hundreds of military officer promotions because his disagrees with the military's abortion policy. One thing that puzzles me is that the his hold could be overcome if the Senate permits the President to make recess appointments for those positions. Thus, the claim that one Senator can stop these nominations isn't correct. I assume that the Senate leadership has decided not to adjourn for a period long enough to permit recess appointments. Am I missing something?

UPDATE: A reader chimes in that the House of Representatives may be holding pro forma sessions in such a way that the Senate cannot recess. I'm not sure if that's true, but I'll look into it.