I'm fairly certain there are taxi stands on the West Side and Marketplace. The West Side location used to be next to the Cirque du Soleil theatre, but that may have changed due to the construction of the NBA Experience. At the Marketplace, the taxi stand is the "old" bus loop. The entrance to that area is near the Rainforest Cafe.
Locations confirmed on this 2016 thread:
https://www.disboards.com/threads/where-to-catch-a-cab-at-disney-springs.3549026/
According to a Disney Mom's Panel, there may be an additional taxi stand in The Landing. I don't recall seeing taxis there, but I also wasn't looking.
https://disneyparksmomspanel.disney...-springs-staying-four-seasons-shuttle-301420/