The reason code compliance is still important is that some codes (e.g. CA codes) require that if you change any aspect of a stairwell, it needs to become code-compliant to today's standards, even if the original stairwell was built before the code was put in place. In some cases, it's actually impossible to be fully code-compliant and you would not be allowed to make the stairwell slightly less dangerous without ripping out major parts of your entire house construction. The only option in that case would be to rebuild the stairwell to the exact same old configuration, to preserve the grandfather exception. I am going through this right now. Here is one resource to help with stairways standards: 2006 Stair Building Code

The edge on the noising looks 'finished'. That's they way it is supposed to sit. It is fine. It is part of what reduces the slip factor on the stairs. It is a physical 'grip' that gives socks a bit of grip. If not, you would be skating down them like a bobsled. It also offers a physical 'hump' or bump to tell your body where the edge of the stair is. This is very important. With stairs that blend into one another (visually) it is hard to tell where one tread ends and the riser begins. This bump helps you find your way up a set of stairs that look like a wall of vinyl.

@hallettco, it's been a long day.....totally forgot the OP said LVP in her first post between my first comment and second comment. I was looking at what appeared to be solid wood in the pic she posted. FWIW, my builder installed red oak treads after we had very light white oak flooring installed and he clear coated them. It's not off terribly but it's been a bone of contention between us. It's not horrible but he gave us a discount so I'm living with them for now :/

For the look you want, the first chouce for me fits the bill. But…..this style home to me doesn’t say farmhouse/ rustic.