Correct, it doesn't seem like they did; the NYT story was debunked.
> dragged an enemy flag through the senate
The rebel flag isn't an "enemy flag" any more than the Republic of Texas flag. It's a historical curiosity that has some function as a completely detached cultural signifier.
They killed a cop? Wow, I only read NYT's retraction of the story, if there was an update on the retraction then it missed my radar. Can you point me to a link from NYT claiming that rioters killed a cop?
To people who are downvoting, the NYT story was made up: https://www.politifact.com/article/2021/feb/22/what-we-know-...