Michael J. Murray and Michael Rea offer the following Thomistic distinction between philosophy and theology:
According to the Thomistic model, philosophy and theology are distinct enterprises, differing primarily in their intellectual starting points. Philosophy takes as its data the deliverances of our natural mental faculties: what we see, hear, taste, touch, and smell. These data can be accepted on the basis of the reliability of our natural faculties with respect to the natural world. Theology, on the other hand takes as its starting point the divine revelations contained in the Bible. These data can be accepted on the basis of divine authority, in a way analogous to the way in which we accept, for example, the claims made by a physics professor about the basic facts of physics.
A "why" question seeks an explanation. Wikipedia notes the following in referring to Aristotle's four causes:
Aristotle held that there were four kinds of answers to "why" questions (in Physics II, 3, and Metaphysics V, 2).
The kind of explanation associated with "why am I here" might be viewed as a "final cause":
End or purpose: a change or movement's final cause, is that for the sake of which a thing is what it is. For a seed, it might be an adult plant. For a sailboat, it might be sailing. For a ball at the top of a ramp, it might be coming to rest at the bottom.
Both philosophy and theology attempt to provide explanations or answer "why" questions. So providing explanations would not be a way to divide them. The Thomistic distinction based on "starting points" may be a more useful way to separate these two activities.
Note that the above distinction of starting points does not prohibit the philosopher from talking about God or Platonic Forms or the One of Plotinus. If some philosopher claims that the existential why is some form of absurdity or that the question is meaningless or that the question shouldn't be asked, these would also be answers to this why question from a philosophic perspective. Other philosophers, such as Martin Buber or Gabriel Marcel, would likely disagree with them.
Murray, Michael J. and Rea, Michael, "Philosophy and Christian Theology", The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/win2016/entries/christiantheology-philosophy/.
Wikipedia contributors. (2019, February 17). Four causes. In Wikipedia, The Free Encyclopedia. Retrieved 12:23, July 10, 2019, from https://en.wikipedia.org/w/index.php?title=Four_causes&oldid=883754450