So there's this interesting scenario.....the House officially ends with the old group on 3 January 2021. On the 4th, the winners of the election will arrive.
Some states will be debated and it's possible that you might have a couple of seats empty because the states haven't finalized the vote. It's also possible that twenty to thirty members might not be there because of a strategy by states to recognize the winners in various elections. It's even possible that one party might start this 'game' and the other party gets into it as well.
On 20 January, a new House Speaker would be elected. It's possible that a major fight brews up out of this mess, and no one can get the votes necessary. Normally, if the President's office is not yet determined (by the Constitution), then the House Speaker would temporarily hold the office until the state-by-state voting occurs.
So if you thought that we had a pretty big mess now....it's conceivable that the mess is ten times the current mess in January.