Streaming on Tubi
It's streaming on Tubi: https://tubitv.com/series/300007146/a-little-princess . Tubi is available on many platforms: web, Roku, Apple TV, Android TV, Playstation, Xbox, etc.
It's apparently the US version. The telltale sign is the opening scene where Barrisford mentions the amount of money he borrows (100,000 pounds) from Crewe and its purpose (development cost). In the UK version neither info is mentioned.
It's surprising that this is to date still the only faithful adaptation of the original novel by Frances Hodgson Burnett.