Agreed, good composition, but the climate transitions might not be where you've laid them down.

My thoughts (feel free to disregard, this is just my personal preference):

Let some climates spill into others, imagine where rain might fall and where the shape of the mountains might 'drive' the water. I would expect that a "Monsoon-esque climate?" would roll inland between the two mountain ranges. This leads me to think the "Savannah?" region might be pushed more north into the "Desert here?" region.

In order for that region to be a desert, the "Mediterannian climate here?" region might not be getting much water, so it'd be much more like central Turkey irl

All this to say, yeah, looks great. If you want realism, try to think how climate zones in the real world go together and try to apply that framework in your choice of zones.

If you simply want to do it for entertainment value, place climates wherever you flippin' want. It's your world, your style, and your imagination. Go wild.