Trouble coming there...
Grooves are a bit too deep really - they should be only 1/2 the depth of the string gauge. But you can get away with deeper ones like this.
Bigger problem is that the edges of the string notches are probably too sharp, so they're catching on the windings. The string should glide cleanly through the notch as you bring up to tension.
Advice here: Bass on its back. De-tension one string and lift out of its notch. With a fine, round file (or fine sandpaper wrapped round a nail...) just round off the bottom of the groove at front and back of the notch. Just a fraction of a mm.
Then get a soft pencil and a pen-knife, and scrape a bit of graphite dust into the groove. Now put your string back and tune up again, gently.
The E string is a lost cause sadly - it might snap when you do this, but it might not .. though that unwinding is only gonna get worse if you don't.
The notches look OK width wise, but they could be a tad tight. That'll exacerbate the problem. If the strings are a tight fit you really ought to get some files or dremel-bits (ideally the right diameter for each notch) and gently widen them so the strings fit perfectly with no binding.
You're welcome.