How to pull headers from a multi-column, multi-row table for a specific cell in the table

Hello,

I am trying to categorize purchase items into different categories. I want to "lookup" each item in an array and then pull the header which represents the category that the item should be categorized under. I don't think VLOOKUP, INDEX MATCH, or INDEX MATCH MATCH allow me to lookup an item across multiple columns and rows and then pull the header for that specific column the item has been found in. How should I be doing this?

List of items that I am trying to look up in my "categorization array" to find category by pulling header of column item is found in:
pic1.PNG

Categorization array (amount of cells with items will ultimatelly be expanded) that column headers/categories will be pulled from:
pic2.PNG

Thank you for your help!