I think most of this is being done because it benefits the Republican Party. Republicans are challenging the election results because they lost an election they wanted to win. Republican are attempting disenfranchise certain minority voters because that group of minority voters does not vote for the Republican Party. For years the Republican Party has supported taking away the right of those who do not for its candidates. Remember, Republicans, like Ann Coulter, have called for laws that would disenfranchise multiple groups (women, immigrants, and youth) that have shown a trend towards not voting for Republican candidates. Remember, in 2016 Ann Coulter for a law that would prevent immigrants from voting if their grandparents had not been able to vote in the United States. Many pointed out to Coulter that a law like that would have prevented Donald Trump from being able to vote in the 2016 election. Clearly, Coulter had not thought out her idea, but the idea was not aimed at voters who looked like Donald Trump; it was aimed at people Coulter thought would not vote for Trump.
Much of what you mentioned is happening because the Republican Party want them to happen. Those things would be happening even if they did not benefit Putin. The actions they Republican Party has been taking in recent years is really about the Party trying to stay in power while feeling they would not be able to stay in power if they did not take those actions. Those actions are not done to benefit Putin; they are done to benefit the Republican Party.