I've used de-waxed shellac under many other finishes, but between coats of anything, I like to scuff the surface some to make the next layer adhere better. For this basket I would use a 0000 steel wool pad, or 220 or finer sandpaper, just to break the shine a bit. It's most important to improve the layer bond in places that could be scratched or rubbed, so what you can reach with the steel wool or sandpaper should be good enough. Then blow it all off with compressed air and put whatever you want as the next coat, so long as this next coat is not alcohol based, like the shellac.
Yes, you did a great job at building the basket. I doubt that I would even try making one.
Central North Carolina