Anecdotal but I'm on a very strict diet, to the point where I have the same thing every meal, every day. There's certain probiotics I take that help bowel movements and some that slow things down. It's very repeatable and given I eat the same thing every meal every day and I'm on a regular eating and activity schedule that leaves very little other variables.
My guess is that for regular people the benefit is insignificant but it's greater for people with issues (dysbiosis).
And the type of dysbiosis you have will determine the effect of the probiotics. For some it can slow motility or cause constipation and others increase motility or cause diarrhea.
There's so many internal variables with your gut microbiome and there's a general lack of reliable methods to test your microbiome. This makes tests like these really difficult and also makes it difficult to treat digestion issues. Because of this, all gastro doctors can really do is slap on IBS/IBS label but not really have a course of action with any decent success rate.
You mean claimed to provide.