I sift my home milled wheat flour. Do I have to sift store bought wheat flour?

I don’t sift any of my home-milled flour, as a rule - but I mill mostly because I like whole grain bread. Hardly anyone sifts storebought flour, as far as I know. What’s your goal? How does bread made from the storebought do?

to make it finer and to oxygenate it. I always add the brown bits back in, usually adding them to the water first before the remaining flour. Some people will soak it longer or toast it to neutralize the enzymes that can break down WW bread.

Some store bought flours like King Arthur in particular I can capture some bran by sifting but most of them are ground too fine to actually get anything. Even still the sifted flour will take on more water it seems to me.