It has sissed, like when you emulsion over silicone, maybe the paint didnt like the white spirit you cleaned the door down with, bad paint ie oils not mixed properly.
Its seems its just up the edge of the shower screen, are you sure the sealant up the inside and outside of shower screen frame is siliconed ?
When you say you have primed it before what did you use ?
You have to be fast when use water based to avoid brush marks, roll doors, spindles, radiators, frames as quickly as you can and you a good sythetic brush to lay off when, try and get as much cool air in the room stops it drying as quick.
No disrespect it doesn't look that smooth, I honestly think the eggshell was drying to quick when you were rolling the walls, and dont roll over any areas you have already rolled.
There newly skimmed walls they dont look too good, you have used too long a pile roller sleeve and have got terrible orange peel effect on the walls.
If the mist coated walls were clean and dry when you started to put the water based eggshell on, I would say you should have thinned the first...
I clean inner of lid completely and always make sure rim has no paint on it, yes I remember the tights, nowadays they do something called paint netz - https://www.mypaintbrush.co.uk/PaintNetz-Strainers
Is it a crime to do that then - I havent spammed with a website or anything, just pointing I have been in the trade a long time so anyone needing any advice I will try and gladly help.
Get the paint mixed at Crown Decorators centre as it is trade paint far superior than buying Crown from b & q.
They have lots of different brushes in there to choose from.
Keep the matt or purchase a scrubbable matt emulsion, dulux diamond matt or crown clean extreme, vinyl silk is so old fashioned, if you want some sheen get soft sheen not the dreadful vinyl silk