Cleaning vs brightening before stain on a sanded deck?

Hello,

We have a 20'x26' deck in the Chicagoland area of unknown age, unknown wood and unknown previous solid stain. We purchased the RAD stripper/brightening kit and the stripper did only a small amount of removal, as expected. We then followed that up with sanding down all of the boards and railings to the bare wood. We also replaced some steps and about 12 floorboards.

My question is, do we need to clean AND brighten, or can we just use the brightener since the deck has been sanded aggressively? OR, do we even need to brighten at all? Can we go straight to staining (We are planning on using AC cedar semi-transparent to stain)? We are letting the boards weather for several weeks prior to staining.

Please see attached pictures, and thank you in advance for your help!