Is there an estimate, and if yes how much climate change will reduce synoptic weather predictability? How will predictability be affected in springtime for mid-latitudes?

Baroclinicity is one factor of synoptic climatology in the mid-latitudes, but it's hardly the only one. Since meteorologists are moving away from traditional forecasting parameters and heading toward a more radar-focused and statistical inference model, it won't have an impact on the "predictability" of synoptic weather. Remember, our advances in science may be the only thing outpacing climate change, and that's a damn good thing.

One more thing: Psychics predict, scientists project.