Although solved, I’m re-opening this topic as I just noticed that iFixit actually included a little warning in Step 7 of their Fairphone 5 instructions for replacing the FP5 display.
This should apply to the Fairphone 4 as well – see their general advice on Press connectors here (Step 6):
It seems to me their final warning against pressing on the middle of the connector is quite important. I have kept doing that before finding the above warning today (and now in fact might have ruined the connector on our local community’s borrowed FP4 
).