Any attempt to suppress "harmful misinformation" will be seen as partisan because, well, it pretty much is. There was a huge amount of utter bullshit pushed on social media about the 2016 election being stolen by fraud, including stuff that the author obviously could not possibly have worked as described or been used to steal the election, and a large proportion of the US population literally believed Russians had hacked the voting tallies. It obviously wasn't harmless either: someone radicalized by Facebook went and shot a Republican senator, and it was only through masses of luck and intrusive medical interventions that he survived. Yet the only thing the mainstream media showed an iota of concern for was the fact that anyone objected to this.
Hell, even in the run-up to the 2020 elections the press were pushing the narrative that it'd be impossible to know the results weren't hacked and the election was valid - right up until it became clear Trump had lost, at which point it became absolutely certain they were valid and the audit chains and processes so robust only a conspiracy nut would question them. The same kinda happened in reverse in 2016.
I'm pretty sure that the "senator" you are naming was Congressman Steve Scalise. I have not specifically heard that the shooter, James Hodgkinson, believed in conspiracy theories about a stolen 2016 election. But he may have.
However the big difference between partisan beliefs about the two elections is this. After 2016, Democrats mostly believed that they lost at the polls due to an effective disinformation campaign run by the Russians. After 2020, Russians believed that they lost due to widespread vote counting fraud. As https://www.rollcall.com/2021/02/24/partisan-voters-claim-we... says, Democrats and Republicans believe this by almost exactly the same margins.
But what is believed matters. Democrats may have been furious, but they believed in rule of law. Radical Republicans, by contrast, attempted to overturn the election via an insurrection.
Hell, even in the run-up to the 2020 elections the press were pushing the narrative that it'd be impossible to know the results weren't hacked and the election was valid - right up until it became clear Trump had lost, at which point it became absolutely certain they were valid and the audit chains and processes so robust only a conspiracy nut would question them. The same kinda happened in reverse in 2016.