It‘s easy enough to believe, but newer research says that the mere presence of a smartphone does not have a measurable effect on cognitive function.
https://www.sciencedirect.com/science/article/abs/pii/S10538...
https://www.sciencedirect.com/science/article/abs/pii/S10538...
So while the presence of a smartphone does indeed seem to impair the working memory, they found "no overall effect of smartphone presence on short-term and prospective memory performance".