Can I paint over wallpaper primer?

My bathroom was professionally wallpapered about 8 years ago, and now I've removed the wallpaper and want to repaint.

Mercifully, it looks like the initial papering was done well and correctly. It came off easily, and I'm left with this odd white-washed look over the previous pink/green/blue sponge painting.

At first I thought this was wallpaper paste, and tried to scrub it off with enzyme wallpaper stripper and a scouring sponge. I managed to get some off, but it was insanely difficult. With further research, I think it's actually something like Sheildz wallpaper primer. It looks like it was applied with a wide wallpaper brush rather than a roller. Does this sound like a reasonable guess?

Finally, can I paint right over the wallpaper primer (if that's what it is) now that the wallpaper is off? Or do I have to sand? Re-prime? Something else?

Thanks!