Is Turing machine a scientific theory in CS?
No, as Yuval Filmus explained, a Turing machine is not a scientific theory.

Furthermore, something can be both a mathematical model and a mathematical abstraction; for example, if the model is an abstraction.

Types of scientific theories

In the physical sciences, a scientific theory is a set of rules or models that makes testable predictions that could potentially be falsified. A Turing machine just isn't any of those.

In mathematics, the word "theory" may be used to describe a framework for reasoning where we have axioms, definitions, and inference rules for making deductions that follow from those axioms and definitions.  A Turing machine isn't that, either.

Personal opinion

I don't think it's a good use of time to devote a lot of energy to these kinds of questions. Instead, I would suggest that you learn the basic material in textbooks on Turing machines and computability and decidability, and don't worry too much about how to categorize or classify it or what words can be applied to it.  From a computer science perspective, it's more useful to focus on the mathematics without trying to put it into a philosophical framework or trying to come up with definitions of these broad, vague concepts (abstraction, theory, model).