New versions of H2 don't have custom data types, they had significant design flaws, security problems, missing basic functionality, and it wasn't possible to maintain any stable API for them.
New versions of H2 support standard ROW value data type and standard ARRAY data type. It is possible to define complex data types with them:
CREATE DOMAIN MY_TYPE AS ROW(NAME CHARACTER VARYING(100), POINTS ROW(X INTEGER, Y INTEGER) ARRAY);
You can also use the non-standard JSON data type.