On July 22, the American Statistical Association posted its biweekly update regarding the status of the 2020 Census Quality Indicators efforts. The update is posted at: https://www.amstat.org/ASA/News/Updates-on-the-2020-Census-Quality-Indicators.aspx, the content for which is pasted below. The next update will be August 5.
July 22, 2021: The task force expects to release the state-level report in the next two to three weeks. It will provide advance notice of the release on the Census Quality Indicators updates page and to those signed up to receive updates. While the Census Bureau has provided all the requested data, the review of the data and writing of the report are still underway.