How should I remove baking soda from my carpet?
If it's not vacuuming out, the issue may be with your vacuum. Check that the bag isn't full and that the brush doesn't need to be lowered for your carpet style.

If you're still having difficulty cleaning it, then I'd consider a carpet shampooing wet vac. They can be rented from a variety of stores and pull out a lot of dirt as they vacuum up the cleaning solution. They will leave the carpet damp so you'll want to avoid walking on it for a day if possible and circulate lots of air through the home to allow it to dry. I'd only do this after you have resolved any sources of other moisture in the carpet.