Yeah the carpet foams are ok and do an ok job of light surface dirt and add a nice smell.
But because this is vomit, you’d probably not want to spray a nice smelling solution over it, you could end up with a vomit smelling floral smell all mixed in(especially in this heat).
What you want to do is to try and remove/ lift the stain (or at the very least dilute it as much as possible with water and a cleaner).
I assume you don’t have a carpet washer, so best thing to do it to run a bowl of warm water and a cleaning solution (can use a number different ones, some carpets (like mine) are even bleachable),
in this scenario id personally use biological laundry detergent, it’s desgined to remove dirt, sweat, urine and food stains from clothing (and vomit is basically food and stomach acid) and carpet is a fabric,, and clean with a cloth or scrubbing brush until the smell either goes or is very much reduced.
Once cleaned and dried, spray the area either with distilled white vinegar OR sprinkle bicarbonate of soda on the area, either of these 2, they are the absolute best natural deodorisers and will actually remove the smell as opposed to adding a sweet smell on top of the sick smell.