Nobody stormed either chamber while members were present. That was Babbitt's mistake.
Once the members were removed, the Capitol police (who have the specific responsibility to protect them) did not use, or even threaten, deadly force.
To prove my point, consider the picture below of rioters at gunpoint spread-eagle on the floor. They entered the direct vicinity of the House chamber around the time when Babbitt and friends arrived on the other side. Thankfully, these guys heeded the warning.
I've lived and worked in DC for over 30 years. My neighbor is on the Capitol Police force. He was called in on Jan 6 and saw Officer Selnick collapse in the Capitol. I don't need to look up the jurisdictions of the MPD vs the CPD.