Doesn't the cleaning solution, also deodorize?
I would not put baking soda on the carpets, then clean it with the "liquid" cleaning solution. It may get, paste-y on your carpets/floor?
The baking soda, will dry differently than jut water/liquid/vinegar.
And, it does not evaporate, off of the surface.
That is why, people vacuum it, not wetting it. If they sprinkle it on the floor.
Once baking soda is 'wet'... it is hard to then vacuum it up, completely.
The vinegar smell will dissipate.
But, on an absorbent surface like carpeting, it may linger more. Because it will not be completely rinsed out.
Also, I don't know the fiber content of your carpets.
Wool, or synthetic for example.
It may damage it.
And not to mention, also having baking soda residue/paste on your flooring/carpet.