Pursuing this question is quite the rabbit hole, but doing research in mathematics makes me believe that math is a science: you have questions, you collect evidence by exploring examples (i.e., conducting experiments), and you formulate hypotheses as conjectures. If you're lucky, your conjectures are correct and you prove them! Proofs are even better than the accumulated evidence on which theories in other sciences depend, in that proven theorems are immune to falsifiability within the axiomatic system in use.
I would say no. STEM is science, technology, engineering, math. compsci is a math degree.
Maybe math is a tool/framework used by scientists? Physics is another example that is largely math.
Math is both a philosophical enquiry (pure math) and a tool (applied math & statistics).
Physics as a science uses math as a modelling and analysis tool.
I've always parsed mathematics more as a language than a science, because it's not necessarily empirical.
Perhaps as a language combined with rules to operate upon that language, transforming true statements into other true statements.