I agree with making them shelves from wood and then make canvas storage baskets that will fit your depth and the widths that you need. I am a big believer in using all the space that you can. No cutting off those back corners for me. lol
Some free patterns here to get you started.
https://www.allfreesewing.com/Miscel...asket-Patterns
Edited to add: I probably don't need to say this, but the bigger the basket, the heavier it will be when loaded with fabric and the harder to move around.
These are what I was talking about, but without the backing being straight on it. I wouldn't put a back on it, but attach the shelves to the wall to utilize all the space.