Would you take plastering advice from a chippy
I did a similar job on a bathroom refurb last year,
knock the high spots off the Artex, you could do with having it tested to see if it contains asbestos, some did and I'm not sure when they stopped putting it in.
Open up the crack, remove any lose material.
PVA ceiling, about 3:1 with water
Scrim up the crack then skim.
If you are not practiced at plastering, ceilings are not a good way to start. I'd get a plasterer in, wouldn't cost a lot and you would get a perfect job.