Well, this is not really the final story, but it's probably the best story one can get from a single survey data source. As I noted a few days ago, the Census has released their 2020 Voter Supplement data, which provides detailed turnout data by demographic group both nationally and by individual states. While the raw data released by the Census in their P-20 tables is quite user unfriendly and does not include time series comparisons, Bill Frey at Brookings has put out a terrific report that takes the data and puts in its proper time series context so we can see how much turnout went up among various demographic groups.
Note that these data, good as they are, are not the last word on the last subject. These data still need to adjusted for patterns in the actual election results, estimated vote preference by demographic groups and underlying eligible voter counts by demographic. In the future the States of Change project will do this and these turnout estimates will be better.