I THINK he's still an Omnic, just a different type. As far as I can tell, 'Omnic' literally just means 'Robot' in Overwatch, so Zenyatta and Bastion are both Omnics. At least, that's what Bastion's backstory seems to suggest imo:
"Originally created for peacekeeping purposes, Bastion robot units possessed the unique ability to rapidly reconfigure themselves into an assault-cannon mode. But during the Omnic Crisis, they were turned against their human makers, forming the bulk of the omnics' rebel army. Following the resolution of the crisis, nearly all of them were destroyed or disassembled. To this day, Bastion units still symbolize the horrors of the conflict."