The protein myth and hype is not supported by the science or data. If you eat a balanced diet you already consume enough protein to fill the .8-1.5 g/kg needed. Beyond that the body can’t process the protein, which is very slow to digest.
The carbs are an absolute must, because your body just burned through glycogen and replenishing within the “glycogen window” is what the real concern is in the 30-60mins post workout. That said it also depends on the type of workout and the duration. Note that not all workouts empty the tank and depending on how you adapt your training to use fat as a fuel source there are other factors that come into play as well.