All the filings and responses are in at the Supreme Court for the USPS's request for a stay of the lower court's injunction that prohibits it from enforcing the new postal voting rules. I believe at this point the next step will the court's ruling, which will come when it comes.
For those following at home, the SCOTUS docket (with all the filings) is here: https://www.supremecourt.gov/search.aspx?filename=/docket/docketfiles/html/public/26a305.html
(Most of the docket entries are amicus briefs from outside parties.)