Yes! I know the book you mean: The Shapeshifter by Ali Sparkes, the first book in a series about Dax Jones.
Dax discovers that he can change shape after becoming trapped in a garden shed. His first transformation leads him to COLA—Children of Limitless Ability—where he meets other young people with unusual powers, including Gideon Reader, Lisa Hardman, and Mia.
It sounds like you remember the story and the characters really well! Who’s your favorite character so far?