I am not sure I fully understand your inquiry. But, I think this may be what you are questioning.

Senate Majority leader is not a Constitutional position unlike the Speaker of the House, which is a Constitutional office. Majority leader is more of a traditional office that is something handled by the Senate in house according to their own rules and procedures. This quick pick of a new Senate Majority leader was to preempt allowing the new Senate membership to make the decision. Their problem was that they were trying to do this on the DL and word got out about what they were trying to do. The Senate switchboard lit up like a Christmas tree with calls from angry Republicans. What the GOP was doing, although it be underhanded, was something they could do according to the Senate's own rules and procedures. It was simply maneuvering by the GOP to have some control over who the next Majority leader would be while they still would have a say - especially McConnell.

Trump ordering Congress to recess cannot take place until he and the new Congress are sworn in and have authority. Till then, the Congress and administration are still in the driver's seat.

The issue of Congressional recess came up several years ago during Trump's previous administration. Trump's plan then was to fire a bunch of DS SES federal employees because that was essentially the only way they could be forced to leave. The SES (Senior Executive Service) was formed during Obama's term. They are permanent government employees that essentially are insulated from other administrations attempts to fire them. Laying them off via Congressional recess was one attempt to rid the government of these Obama DS hacks. Good old Mitch McConnell thwarted Trump's attempt by refusing to call a recess. The dates from the Q post would apply to that particular incident because Trump was already in the WH - but not to the current situation due to the above forestated reasons.

Bringing Congress to an official recess is very rare because it is a pain in the a**. Most of the time what is called recess is not. Congress essentially adjourns and leaves a skeleton crew in place just in case some emergency occurs. There are several formalities involved to shut Congress down in a real recess and formalities that must be taken to readjourn. This is why they don't do it. Should a crisis occur during a recess it would hamper Congressional ability to act until they were formally readjourn.

Most of us on this forum have had to take a crash course on how our government actually works - something that for many was neglected deliberately as part of our education system - especially for younger Americans. No harm, no foul. It is a learning experience for everyone.