The basic idea looks pretty much fine. Parallel coastlines, bands of grassland, large forests and a large mountain chain pretty much work. And mostly leaf forests and a few mixed/coniferous forests near mountains is good too, but you can apply that to the smaller mountain chains too. The idea I get from this map is that most rain comes from the south west. Then the leeward side of the mountain chains could look drier, unless you have rivers running there.
But you could depart a little more from the basic idea to make it feel more lifelike and less schematic. That coastline is pretty regular, you could break that up with a few peninsulas or islands. And I can't see if those are beaches by the coast, but then you could have different terrain there too like dunes or coastal cliffs.
Maybe the idea is to keep the different terrain types managable and avoid scope creep. If that's the idea, the general idea works and it's perfectly fine. But theSwish's suggestion to add hills, highlands, wetlands and lakes is one to keep in mind if you want to add more. Drier grasslands like steppes or savannas can fit near that desert or in the leeward sides of mountain chains. Meadows or heathland can be added near forest or shrubland.
I think the number of rivers is low. You'd expect more coming from the mountains, especially the Forbidden Lands. And you could develop the river mouths more and go with different types like deltas, estuaries. It's okay if 1 or 2 rivers really dominate the water inflow. Unlike what theSwish said, "one river coming out of nowhere" isn't odd if it's pretty wet grassland, but you don't want too much of that and they shouldn't be too wide. And again, more lakes and wetlands.
The map does look really empty though. Maybe it's a setting where a region that's been settled only recently. If that's so, you could have much more forests or shrubland, above all in places far away from civilisation. The amount of grassland looks like the region is pretty heavily grazed or deforested. And the location of settlements is a little strange. Most are at the coast, like you expect, but only 1 is at a river mouth if you stretch that concept really generously. You'd expect towns at each river mouth of a river with settlements. And more town on rivers. Water routes are the cheapest transpost routes. So settlements should follow that pattern, especially if it's been settled recently by seafarers.
I'm a bit thrown off by the scale. You see single buildings on one hand, but some mountains look like they are only like 10 building big. That could be an artistic choice. But it classes with the invisibility of farmland. Fantasy videos kinda suck with this, but you expect visible crop fields for miles around a big town. Near or (partially) in every town, you should see a few acre of cultivated forest, then orchards or vinyards preferably on higher ground, and then fields with crops. Farmland should roughly follow the patterns of rivers and roads, because transport. You can leave those forests near the towns in the south in place though, people don't always clear them.
tl;dr: more water, slightly more irregular coast, actual river mouths, more settlements near rivers, maybe more forests and maybe more terrain types, remember the pattern of forest-orchard-cropland.
