This claim is not true. On the Starbucks website, under their sustainable initiatives, there is no mention of any initiative to phase out dairy. Rather there are initiatives to cut down carbon emissions through focusing on plant based offerings, making these offerings more accessible to customers. They intend to make it more accesibble by making plant based offerings free to substitute for dairy products. Additionally, they have invested in sustainable dairy practices rather than cutting down dairy products.
https://about.starbucks.com/stories/2023/starbucks-furthers-commitment-to-sustainable-dairy/