I have this issue as well. Hard to catch sometimes too.
When I went looking for an answer I found this post. Apparently this was addressed a few years ago.
https://forums.sketchup.com/t/model-styles-in-layout-not-always-rendering-correctly/48858
That said, the behavior is not ideal because if you use multiple stacked views in your workflow that have different styles you have to reapply the custom style to each viewport. Why have the option to change it if it won’t respect that change when copying and pasting a viewport.
The solution proposed was to have multiple scenes in Sketchup. With complicated projects this would necessitate so many scenes that it would be hard to navigate. Making the changes in Layout is far easier. I can’t even imagine the size of the dropdown if I added in all the scenes I’d use in sketchup.
A ruby script to toggle the style to a different one and back might solve this temporarily, but IMO this is a bug that should be addressed by the sketchup team.