The gut microbiome is a hot research area, and probiotics are increasingly marketed to athletes for immunity, gut comfort and even performance. The evidence is promising in places, but far from settled.
What seems reasonable to say:
Effects appear to be strain-specific, so results from one product cannot be assumed for another
Some studies suggest certain probiotics may slightly reduce the number or duration of upper respiratory infections in athletes, but findings are mixed
Evidence for direct performance benefits is limited
A diet with plenty of fibre, plants and fermented foods supports a diverse gut microbiome without supplements
If you want to try one, practical points: choose a product with the strain named on the label and some research behind that specific strain, take it consistently for several weeks, and start well before an important trip or race, not the day before.
Some people get temporary bloating at first, another reason to avoid starting close to competition.