The Pinterest picture is high quality shelving that was likely professionally installed and cost several thousand dollars. You won't get close with construction grade lumber and drive yourself crazy in the process.

Pick the best pieces of lumber you can find and accept that.

I would like to use wood, paint it white, needs to be sturdy to carry my jars, need to look organized and not messy

Nowhere in there did you say "must be sanded smooth like fine furniture". This is organizing a basement wall to make more storage, not going in your living room.

Find straight boards, as smooth as possible, to fit your space. Paint them white, and build the shelves without the birch facings and the other expensive stuff.

I think 3/4-inch-thick is fine for a vertical support. Most boards don't compress or break or sag when weight is on them vertically. As long as they can't slip out of position, I think they'd be fine. Especially if you space them as you have--that's close together.

Or course, you have 2x9 on the bottom. How much do you care about having the width change on the higher rows? You could rationalize it by saying that the lower row has the widest support to create a nice base.

One other difference between what you're doing and what the Pinterest pic is, is this:

In your example, and continuous boards are the VERTICAL ones; in yours, the continuous boards are the horizontal.

I don't know which is better. You'd probably have more sag with a wider span.

As for smoothness--prime and paint one of those 2x9s. See how much the paint smooths it out. This is just "trim and tidy basement storage." And remember that only the front edge wiil really show.