Hi Adi,
Compared to my electric guitars, this low E string is already way deeper in the nut slot. Seeing the rough edges on the close-ups, I guess someone has already done some filing on this nut. If a proper restringing doesn’t help, I’d try a brand new nut.
I found a few videos and articles that you may find useful:
Easy Stratocaster mod: How to replace the nut on your guitar
Does this bone nut fit my guitar?
How to fit a preshaped nut on a guitar
How to Make a Guitar Nut from a Blank
How to make a string nut for the first time
Gauged Nut Slotting Files
Making a Nut, Step-by-Step
Making a Guitar Nut: 3 Tips for Proper Slotting
How to Fix a Low Nut Slot Fast