Yes: he's filed suit against the "Center for Countering Digital Hate", also for publicly criticizing the way he runs Twitter.
https://www.techdirt.com/2023/08/01/free-speech-absolutist-e...
https://storage.courtlistener.com/recap/gov.uscourts.cand.41... (plaintiff's complaint)
https://storage.courtlistener.com/recap/gov.uscourts.cand.41... (defendant's anti-SLAPP motion)