The Dem controlled House will definitely have anti-civil rights legislation on the agenda. "Universal" background checks will certainly be on the agenda. Some form of "assault weapon" ban is certain. There will be other measures such as magazine capacity bans and there will be stealth de facto bans like major excise tax increases on ammunition.
But, the real focus of the House will be all Trump, all day. Oversight hearings on all the cabinet agencies, attempts to reintroduce Obama era measures that Trump rolled back, and impeachment is absolutely certain. In addition climate will be a major focus and time waste. Loons like Ocasio-Cortez will be pushing carbon taxes and vast new subsidies for wind and solar as well as punitive measures designed to slow and damage fossil energy production.
So, new mass shootings will deliver substantial anti civil rights legislation but most of the Dems focus will be Trump hate and climate charade. Everything the House passes has to go to the Senate. Very little of the large amount of legislation passed by House Republicans in the last four years has been passed in a Republican controlled Senate, so the risk of major anti civil rights legislation being passed by the Senate, baring another Sandy Hook type event, is very low. Were anything major passed, a veto is almost certain and a two thirds override almost impossible.
There will be much sound and fury, many illegal messaging bills, a great deal of pandering and signaling of virtue and, as is usual with Congress, nothing will get done.