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:
https://www.pacermonitor.com/public/case/40480193/Hobby_Lobby_Stores_Inc_v_Obbink
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The Early History of the Codex
Thoughts on History, Religion, Archaeology, Papyrology, etc. by Brent Nongbri
Everyday Stories from the Ancient Past
Patristics, Apocrypha, Coptic Literature and Manuscripts
Pedagogical Approaches to Palaeography and Codicology
Thoughts on History, Religion, Archaeology, Papyrology, etc. by Brent Nongbri
Thoughts on History, Religion, Archaeology, Papyrology, etc. by Brent Nongbri
Thoughts on History, Religion, Archaeology, Papyrology, etc. by Brent Nongbri
Variant Readings 
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.
https://www.pacermonitor.com/public/case/40480193/Hobby_Lobby_Stores_Inc_v_Obbink