Solved it. It was because files names are case sensitive on Itch's servers and my image folder had a capital "I", but my path names did not.
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I uploaded a ZIP file for my HTML interactive story (written in Ink): https://jejboulet.itch.io/hunting-for-treasure. The story displays, but my images do not and I don't know why. I have tried it in multiple browsers.
Before uploading to Itch, I tried out the story directly from the index.html file in my own browser and everything worked fine, so it shouldn't be an issue with relative paths.
I tried to replicate what I did before in my other uploads: https://jejboulet.itch.io/chat-jouer and https://jejboulet.itch.io/the-curious-little-lamb. Those other stories seem to work fine for me in my browser.