I ran into the same situation myself on a 6S Plus I was fixing up for my granddaughter.
Turns out there are two sets of LEDs along the top edge of the screen that serve as the light source for the backlight, one on the left half and one on the right half.
I can say fairly definitively that the right half set of LEDs is out on your phone, because that's exactly what mine looked like.
I messed around with mine quite a bit but didn't have any luck getting it to light back up again. It's theoretically possible to replace the backlight, but very difficult; I had an old broken screen I used as an experiment and ultimately wasn't successful in disassembling it far enough to replace the backlight without damaging parts.
Having given it the old college try, I ended up ordering a new screen, which fixed the problem. Given the age of the phone, replacement screens are getting very cheap; they're averaging about $15 USD on Amazon, and can be found even cheaper if you shop around at places like eBay and AliExpress.
Anyway, yeah, try cleaning the display cable; that's the one that carries the backlight power. Check both sides carefully with a magnifying glass and a bright light for any bent or broken pins; bent pins can occasionally be straightened with fine tip tweezers. Check the flex cable for any signs of damage as well.
If nothing helps, then ultimately the fix is going to be to replace the screen. Obviously you already know how to do that, so I'll dispense with my usual habit of linking to guides.
Good luck; let us know what you find!