Do you know what the specs of the display are?
No, this is the first time I use a display, so I don't know how and where to search.
I hope when disassembling it, I will find a labeling inside leading me to a datasheet.
And what data do you want to show on it?
I'm fine with simple data about how much the battery is already charged, e.g. a number between 0 and 100, where 0 means empty and 100 means full charge.
There has been a state of charge indication on the original display, but it is too rough (only three degrees of charged amount), and also might be rather complicate to trigger.