Chosen Solution

I was putting the original screen onto a iPhone SE but forgot to unplug the battery so as I replaced one of the connectors there was smouldering. The iPhone now won’t turn on. How could this be repaired/what parts could be replaced to fix?

You’re free to try your luck and buy a replacement screen but chances are it won’t be sufficient to fix the phone and you may easily end up throwing money. Backlight rails are high voltage and when shorted may cause extensive damage. It would be best to hand it over to an experienced microsolderer for evaluation but unless you have important data you need to backup a repair might not be an economically interesting alternative with a used SE.