I see that AH Datalytics has published the inaugural version of their Real-Time Crime Index, which provides rough estimates of crime within a couple of months of it happening. This contrasts with the FBI, which takes about six months to provide quarterly estimates and nearly a year to provide final annual figures.
What's more, the RTCI provides monthly data. For example, here's their estimate of murders over the past few years:
Does this give us any insight into why murder increased sharply in the spring of 2020? Maybe....
Up through April 2020—when COVID was already in full swing—murders remained at normal levels. They spiked in May when George Floyd was killed and then spiked further in June. But then they declined rapidly even though COVID was still surging.
So this suggests it was George Floyd, not COVID, that caused the murder spike. However, the annual summertime murder peaks have remained high for three years. It seems unlikely that the George Floyd effect could last that long, while the COVID effect probably could.
So it's still very difficult to say. If I had to guess, I'd say it was mostly COVID but with an extra little surge in 2020 when Floyd was murdered. It's just a guess, though.