An anonymous commenter links to the resource below, which appears to show some developments in the civil case against Professor Obbink. I have not accessed the documents in the linked here, as they are behind a paywall:
Here’s one of the documents: https://www.courthousenews.com/wp-content/uploads/2021/06/hobby-lobby-oxford.pdf.
NY Times Sept 24:
The latest document in the case (September 13) is now posted on https://www.courtlistener.com/docket/59954890/hobby-lobby-stores-inc-v-obbink/ (direct link: https://ia802308.us.archive.org/14/items/gov.uscourts.nyed.464996/gov.uscourts.nyed.464996.7.0.pdf ).
It seems Obbink failed to enter an appearance and file an answer by the deadline. On Tuesday (11/30), the court clerk entered a notice of default. Essentially a win for Hobby Lobby.