The reason for the confusion is because, now that I have looked more, the email claims 2X23 on outbound and 1X23 on return, but online booking still shows 2X32 both ways.

Route is TLV-FCO-JFK-FCO-TLV; Y+ for FCO-JFK and Y for other 3 legs. (Also weird is that after a change in schedule, my EWR-FCO is now showing me as seated in row 15 of a 777 (Y+) though on the seatmap, if I want to change seats, I can only choose from 18 and on (Y).

Ticket was issued in November, IIRC. Was done directly through AZ.com and all legs are operated by AZ.