Cruz, for better or worse, was trying to get an election commission to examine how the vote was counted and how the laws of voting were set up around the nation. Not a bad idea, in and of itself, but it did not belong in the Certification of the Electoral Votes. Bad timing on his part.
Hawley, calling out Pennsylvania's may have had merit. If my understanding is correct, the following was the process that happened. Pennsylvania was in the midst of passing a Constitutional Amendment on voting. In Pennsylvania it takes a vote of the legislature, then in either the next year or the next legislature, it must be passed again. Then it must be voted on ;by the people. The first vote in the legislature had occurred and the amendment had passed. What occurred in Pennsylvania, to my understanding, is that the second passage and the public vote had never occurred. Instead the Democrat governor and the Democrat Secretary of State, together with members of the Democrat party agreed to implement the amendment during the pandemic. It is a defensible idea, but it goes against the State Constitution and makes a mockery of the rule of law. Therefore Pennsylvania's votes should have been thrown out, given to neither party, in my view. Trump receives none, and Biden ends up with 286, more than enough to win the Presidency, and both the National Constitution and State Constitutions are upheld. If my understanding is wrong please show me where.
As for the Republicans ending as a party, that is entirely dependent on how the Democrats operate in Congress. If the likes of AOC, Pelosi, Warren, or Sanders are the major movers they will be back even stronger than before. We do not know what the future holds for the party, but it's future seems to depend, at least for the moment, of what the Democrats do, and not what the Republicans stand for.