I feel your pain as I did the same with my stainless steel oven. I rubbed some oil gently on it and it did help, but the t cut idea sounds good!

Do you like patterned tiles at all? Doesn’t have to be garish and you can keep the pallet simple. I’m thinking tile the whole wall, the same width as the vanity unit, up to the ceiling, similar to first picture. Or if that’s too much, then just tile the space from the sink to the mirror. I would raise the mirror a little so that it doesn’t get too splashed.

I have tiles on one wall by the sink, and mirror in a darker area. I also have wallpaper over the other (non-cooking) side of the kitchen. It's great!   Do what works for you.

Are you having wall units? If so you can have the backsplash up to them. If no wall units then 60cm is plenty enough with maybe a taller bit behind the hob. A picture of your kitchen would help us advise better.