I think what's key as allies is taking the back seat and supporting. Listening. Amplifying black voices.
As Brittany Packnett Cunningham (@mspackyetti) keeps saying, "We Save Us." What we as allies can do is continue to educate ourselves and our non-BIPOC friends and family. Donate to causes and as I said before amplify black voices.
Also, taking care of mental health right now is SO IMPORTANT. I feel like even the most "solid" people right now are feeling this strain, let alone people affected by anxiety, depression, etc. You're right that this is not something we "move on" from and it's important to continue to stay engaged and keep supporting this movement. That being said, I've been reading it's healthy to limit your social/news intake to a designated time and cap it off so you are not incessantly refreshing your feed and building more and more anxiety.