As you noted Cinbal, Levissi, also Bulent's Gozleme, Yalcin and Caspers are all open
Izela has opened and I expect Sarnic to be opening in March but I will check - both best to ring and make a reservation before you turn up. Blue Butterfly with the garden and an inside section has also opened.
Muzzy's has been looking very busy these days.
I have not seen much happening at Antique or Poseiden and have not heard if Kalymyssoss has opened or Istanbul
but early April sounds likely especially considering the filming planned to be going on in March. Possibily not Kaya Wine house or Jazibe I guess.