The only two methods for removal of a cabinet officer are for the president to fire them or the congress to impeach and convict.

Since Biden won't, an impeachment and removal is the only option and would be a mark against Biden and possible bolster to a Biden impeachment.

The simple truth is impeachment has lost it's impact. Up until Clinton it had only been used twice on top level persons. Once against President Andrew Johnson and once against a Supreme Court Justice. In both cases they were not convicted in the Senate. It's a pretty much drastic last option.

(There have been many lower level impeachments of federal judges, though, for obvious crimes such as bribery)

The mere threat of impeachment was enough to get Nixon to resign even though he had committed no crime. His deal was the withholding of evidence from congress, which is not in and of itself a criminal offense.

Clinton survived an impeachment where he actually did commit crimes. And politically ended up wearing it as a badge of honor.

Then Pelosi rammed through not just one but two kangaroo court impeachments of Trump and the whole world saw them as the farce they were.

So, IMO, this will end up going nowhere as the Senate now has the greenlight to not take it as it should be, a serious constitutional duty.

Our fidelity to the Constitution and even the Constitution itself has become of no more use than toilet paper.

Modern day Rome except the enemy isn't at the gates they are running things.