A sisal rug by the sofa area will work well with the green carpet. Also a sheepskin by the play area to lighten and break up all of the green.

How about a 1/2 wall to hide the toys and make a little play area for your children? Can't see exactly where the corner is that holds the toys but the children might like their little play area....house? fort? store? Lots of potential for imagaination.

I wouldn't build a wall personally, but if you wanted you could create a divider with a low bookshelf in the play area. The toy bins can be put on it as well as books. And the kiddos can push it out of the way for games and setups that need more space.

I'd move the train table over to the toy side of the room, pull the sofa forward, and add a proper wood coffee table. It can be used for colouring, board games, or drinks/snacks.

Then move the black dresser to the wall where the art is and add a low wattage lamp for lighting during movie time. You could paint the dresser white if you wanted. Move the art to the wall in the toy area and hang it lower.

In the corner where the black dresser was I would add a small table, maybe 3x5, and four chairs. The table can be against the wall for everyday, to be pulled out when needed for board games, puzzles, colouring. You might even install floating shelves above it to store those games and puzzles.

Since you have to live with the green carpet, I suggest trying to incorporate it more. A few subtle hints of green can be introduced in other decor. I think this will go a long way in making it work as it will move the eye around the room rather than just focusing on carpet because besides toys it’s the only colour in the room. You could do this by adding wallpaper to back of bookcase shelves, pillows, throws, lamps, and art.
I would designate nook area behind sofa as kids area by decorating it as such. You could play up the green carpet by seeing it as the grass and adding flower or tree decals/ stencils to walls. Make it fun! Your sofa looks like it could be moved forward a bit and center it to the wall unit if it isn’t already. Curtains on the taller windows and some plants would also make it cozier.