Be very careful if you use that baking soda detergent mix. I used it (measured to a T) and it made my carpet permanently crunchy where it was used and it has never felt the same. Doesn’t look too bad or bleached/discolored - just looks stiff and feels gross when you walk on it (thank goodness it is more in the corner and not where I walk most of the time). My carpet is a frieze so maybe that type just doesn’t work well with this solution? I don’t know. Definitely spot test.
Like @RPM I use Woolite. I use a different type though, the Woolite Fabric & Furniture Cleaner Foam which has a scrubby bristly head on it. It works wonders for poop stains and vomit. It is honestly magical for me - very little effort to get things looking and smelling like normal! I use it in my car with a medium grey interior and my carpet which is beige and it has not left stains on those.