Countifs with dynamic criteria and wildcard characters

Hey folks, I'm new as a poster to this forum and would really appreciate your help!

Problem:
I have an array that has numerous text strings in it, seperated by commas. I need to count the number of occurances of a certain text string in the array, and to do so in a way that avoids me having to manually type in the text string each time.

I've attached a sample showing an example data set, and the way I do it now (manually typing it). I believe that part of my problem is when I make the criteria in the countif dynamic, I lose the ability to put the wildcard characters.

Goal:
To be able to have a formula where I can make it link to a cell containing a text string and it would find all occurances anywhere any given cell within an array. Please see my sample.xlsx to see what I am working with.

Thanks in advance! I really appreciate it!

Amazing - that worked perfectly. Thanks a ton Martindwilson. Really appreciate it!