Looks like a fun and creative space. You don't need to pull everything out of the room. Measure the space and the wall areas. Just jot it down on paper. Measure the book shelf units and the sewing table to determine where they will fit into the space.Like a puzzle, there is only so much space to fit it all in. Work with the lines of the space.
Organize one area at a time. Set small goals for each day and it will soon be done. Put similar items together so there is continuity to the space. Move all the bins with the other bins onto the units that hold them.
First, Is there a view out the window? I would claim that space for the sewing desk. Move out the large white shelf unit. Add the wall peg system to that area in a large grid.
RE: The white shelves for bins under the eaves. Is it one that can be rotated? What is the current height of the shelves? Approx 30 inches? Put it upright and move to space between the drapes and the eaves.
Move all the plastic storage units under the eaves.
Clear off the wood book shelf unit and use for fabric storage. Move it to the wall where the sewing desk is now. Ruler fold the fabrics as they will store easier. Are you using the bins for storage? Ruler fold to the size of the bin. Lay the bin sideways so you can see the stack of fabric. No need to pull the bin off the shelf when selecting fabrics as you can see them all.
You may find after organizing that you don't even need the wood book shelf in the room. Good luck and tackle the room with small goals each day. Please show us "after" pictures.