Hi, I had purple suede effect on my wall. Easy to sand the texture off. Talk to your paint shop about the right colour undercoat/sealer to cover a dark colour before painting your new colour on with 2 coats.

I like the colours you’ve suggested. I find neutrals restful. Do you have a sample of your cabinetry? An easy way to get a coordinated look, without whites clashing, is to have the white colour matched at the paint shop to the cabinetry. The colour match will tell you if White Beach is on the right track. I’d consider a more plainer white for the trim ie Natural White as suggested above or Berkshire White. For your splashback - could the budget stretch to the benchtop material? If not a tile colour that picks up one of the benchtop fleck colours will give you a coordinated look. Sounds lovely. Come back and post the completed pics.

I agree with both your painter and your Google result. The issue is something that has soaked into the surface of the old wall, particularly as you had an odd result when cleaning. You can’t expect the painter to sand and paint as part of the original job but they may be able to offer advice and action if you’re prepared to pay them. If you want to DIY I’d be sanding the wall and trying some stain locker undercoat.

The best way to cover dark is to use a grey tinted primer first. Talk to a paint specialist. Dulux on line may help