Hello! I apologize for the very delayed response here. I haven't been on Medium for a while.

Were you able to get to the bottom of your relative file path issue? I just tested this out by adding a test.html file to my github.io repository (https://github.com/emilymdubois/emilymdubois.github.io/blob/2dadb42ab4fab209bdd81662bb7ebecfa972ea6d/test.html), and it was available on my Squarespace domain about a minute later (https://emilymdubois.com/test).