I think you should definitely tile past the cabinet up to the corner where the sink cutout happens. Not so sure about continuing around the corner. It might depend on the tile color.

Tile the corner.

End tile at the edge before going around corner. Leave the area around the corner plain. How messy can that small area get? Shouldn't be hard to keep it clean.

Honestly, I don’t think I’ve ever splashed that side wall, so keeping that clean will be no issue. I’m more concerned with what will look the best. I haven’t found any pictures with a similar set up to see how it should look.
We have laid tile multiple times (2 bathrooms and the kitchen tile), and I have used both Schluter and bullnose. I think the Schluter strip might be too contemporary for my kitchen, but I’ll see what tile I end up choosing, as not everything has a matching bullnose. I don’t plan to pick out the backsplash until I’m certain of the countertops I want so I can make sure it all flows together. Thanks all for the suggestions!

Show us the other end of the sink.

Here are some more photos from further back.

I don’t think I’d tile around the corner.