Unfortunately, the baking soda reacted with the wood and has "weathered" it. I don't think there is a way to fix it other than covering all the wood up with paint, a dark stain, or, applying a baking soda mix to everything so it matches.

Baking soda reacts with tannins in the wood. Pine doesn't have tannins that I'm aware of.

I cannot tell if the wood is indeed pine, or cedar, or something else. Looks like the wood just has a linseed oil finish. But linseed oil would not bring that much color out of pine. If it is pine, most difficult thing would be matching the color.

You may be able to sand it out.

After wood is thoughly dry try a "card scraper" which remove's more wood and faster than sandpaper. After getting the strange colors gone it will be simpler blending fresh new pine with aged pine than changing colors presently showing.

" I used a baking soda paste to remove it"

Something the "chemical-free cleners" promoters don't like to admit is
that on the wrong surface, the "mild" cleaners are damaging. Maybe in a
non-toxic way, but cosmetically damaging. The alkalinity of the chemicals in the baking soda discolored the wood, and the water in the paste didn't help.

If this happens again, scrape off as much crayon as possible and use Goof-off or other solvent based crayon removers. They are less likely to attack the wood.