Personal opinions: I do not think there has the most authentic definition in academia because everything you will learn is highly subjective. I studied Education in TESL when I was a BA student, I would recommend taking a look at Professor Dr. Arshad Samad's book in ESL teaching and learning. Also, I think Brian Tomlison has some easy to understand and undergraduate-level textbooks about pedagogical grammar. If possible, try to understand grammar from applied linguistic perspectives, I personally think it is very very helpful. After all, you will form your own unique worldview in your field.

Pedagogical grammar is designed for teaching and learning a language, focusing on rules, patterns, and explanations that help learners use the language effectively in communication.

Thanks Muhammad Amjad Bashir