I am trying to submit an exercise (ax model). I have packed the image into the .blend file as requested in the exercise, …

Hey, the texture is not a part of the model, so whenever you export something to another program or viewer, you’ll need to upload the texture separately as well. Here’s how to do that for sketchfab: https://help.sketchfab.com/hc/en-us/articles/202600873-Materials-and-Textures

Only Blender opens .blend files – other programs like Sketchfab or Unity that support the .blend format are actually taking the object and automatically converting them to an FBX behind the scenes, which does not automatically take the packed image textures with them.

Additional info about exporting to Unity: You need to add a material to your object in Unity then add your textures to that material(Drag diffuse image to “Diffuse=”, drag uv image to “UVmap:” etc)  in order to texture your model.