There’s no clear connection between low carbs and probiotics. Not everyone benefits from either intervention, and some people benefit more from both than from one. These are fuzzy interventions that are tricky to evaluate, requiring patience, consistency, and objectivity, and they don’t tend to completely eliminate episodes of pouchitis, nor are they likely to completely eliminate the need for more definitive treatments (e.g. courses of antibiotics periodically). They may reduce that need.
That being said, if probiotics are more tolerable for you than a very low carb diet then it’s probably better to try probiotics first, and get aggressive with them before considering the diet change. It’s also okay to choose a more liberal diet and accept the possibility (not certainty) of a more frequent need for antibiotics. *All* of this is intended to help you feel and function better, so your preferences matter a lot.