When it is not an election year, and when we don't have COVID screwing up the normal order of things, appointing a new Supreme Court Justice has been, political theater and high drama, particularly in recent decades.
The entire idea that a Justice should be someone with the personal integrity to rule on the law, and not involve their own personal views on ANY matter seems to have been lost in the hubub about "where they stand on issues" and "Litmus tests" or them not, perhaps, being pure saints in their personal lives before becoming a nominee.
No one with any desire to be some degree of "activist judge" should ever be considered for such a position. However, we get the choices we get, and lately it seems pure partisan politics counts for more than the rule of law and the duty to the American people.
The sitting President has the duty and responsibility to nominate a replacement when there is a vacancy. NO ONE ELSE DOES.
All cries for the President to wait until after the elections are the ravings of whiners who are not currently in power to make the needed decision, but HOPE to be in that position to nominate THEIR choice AFTER they win the election.
The Pres COULD do that, but is under no obligation, legal or moral to do so.
Personally I don't think he should wait. DO BUSINESS as usual without pandering to the political opposition, but, that's just my opinion, worth what you paid for it.