I did two test charges today with the new Tesla CCS adapter and two with my old Tesla Chademo adapter, first at a Flo station (75kW max) and second at Electrify America (150/350kW). The Flo charge was first with a relatively cold battery (ambient temp 63 degrees, 5 miles of driving) and state of charge around 55%. I pulled around 50kW on the CCS, 18kW (?) with the Chademo.
Then I turned on preconditioning (navigate to a local supercharger), but diverted to EA. I tested the 150kW and 350kW CCS chargers and got ~70kW with each (SoC ~60%). The EA Chademo gave me 43kW. Then I drove 1/10 mile to a V2 supercharger and got ~70kW as well.
So both adapters will work with a 2023 Model Y. The CCS adapter requires CCS enabled (obviously); the Chademo adapter does all the signal conversion internally and does not require any explicit support in the car.
