You don't get it. Its not about where one academic subject sits versus another or how they are taught. It's about the function they both play in daily life. We have science as we have it today because of the developments in philosophy that we have had.
There are 5 fundamental branches of philosophy that attempt to answer 5 questions.
What is real? (Metaphysics)
How do I know? (Epistemology)
Who/what am I? (Human nature)
How should I live? (Ethics)
How should we live? (Politics)
In modern society we have taken to answering the question of "how do I know?" by the scientific method. Well, a lot of us have.
Think about recently how the replication crisis has affected our philosophy. We have started to question the methods efficacy in certain disciplines and we are going back to the drawing board. Back to finding a way to answer the question "how do I know?"
Developments in philosophy form the bedrock of daily life. Science is included in that.
My argument is that these branches are not sibling branches.
Metaphysics sits at the root and all the other branches are abstractions on top of that. Like really high on top and centric to the human experience. It's as arbitrary as putting "dog nature" in place of human nature, what justifies human nature to be the foundation as opposed to "dog nature"? Nothing. Hence my argument for why this grouping and the field itself seems illegitimate.
Well if dogs were smart enough to figure things out they'd probably put dog nature at the top as it would be their experience they are trying to make sense of.
Everyone has their own answer to those questions. That's their philosophy. The field itself catalogues developments in which answers have been a) novel and significant and/or b) become widely accepted at some point in history.
Sort of the whole point of it is that not everyone comes to the same set of answers. So, dialog ensues as people try to shore up their viewpoints with one another and both are often transformed in the process. That's how a dialectic works.
Before the age of enlightenment, yours was not a commonly held viewpoint. After, it became to be acceptable and then accepted. That's philosophy at work.
I don't think of it as a foundation per se. It's more like a continuous process that carries out over time as individuals interact, the result of which only a small portion is obviously visible with the rest going mostly unnoticed.