SageMath is much broader than SymPy, by integrating a lot of third-party niche tools that have been developed for decades, often as C libraries.

Unfortunately, SageMath is not directly usable as a Python package.

That's where passagemath [0] comes in, making the rich ecosystem of SageMath available to Python devs, one package at a time.

[0] https://github.com/passagemath/passagemath

Sympy is part of SageMath. SageMath is just a kind of user interface to Sympy and a bunch of other Python libraries. Mathics I haven't tried.