Short answer: Deserts in the west, south and in the center, rainforests in the east.
Mu is roughly located between the horse latitudes at 30° north and south. Around this latitude, conditions are very dry, because the air is descending in these areas, warming up, and getting drier. The opposite happens at the equator. Here, the air is ascending and getting colder, which leads to condensation and rain. This is why rainforests are so dominant at the equator, except in high mountains.
If I see this correctly, there is a high plateau in the center, so the air has to rise before it gets there, loosing most of its humidity before it gets there. This is not the case in the east, where the terrain appears to be flat. Also the prevalent directions from the trade winds bring a lot of humidity from the ocean, so conditions there would be similar to the Amazon basin. Conditions in the south and west are probably similar to the center. According to the map, they also seem mountainous, leading to a lot of rain directly at the coast (maybe some rainforest at the hillslopes close to the equator) but almost no rain as soon as the mountains are high, with a climate similar to the Andes.
The north is quite dry due to the location around 30° N but is is flat and located close to the shore, so it might experience seasonal rain when atmospherical zones shift with the seasons.
The Isola di Pasqua is a bit complicated due to its location at ~30° S but directly affected by the trade winds from the east. I would expect humid conditions similar to Florida or northeast Australia in the east and drier conditions with a rainseason in the west of the peninsula.
Note that this continents is much bigger than Europe. This map appears to be a mercator projections, which greatly exaggerates the size of landmasses far away from the equator (i.e. Europe). I agree with @JBH that it is close to the size of North America.