I have the same camera and you can choose to shoot lossless compressed to help the whole process and use Capture One for Fuji to edit. It’s really light, I think, and it’s free. Give it a try.

It’s pretty simple: OLED works in a very different way compared to LCD. So when you edit the highlights and the shadows especially they will be represented in a different way on an OLED display compared to an LCD. Also you don’t know what color gamut your iPhone is using but it’s most likely DCI-P3 so yout photos will look awful.

On my phone I’m pretty close to sRGB so, even if it’s an OLED, I get good sRGB reproduction. Maybe try to edit one in different color gamut settings to figure it out.