I tried several different options (several hours) and until scrollbar-theming has some default way to be changed, this works:

:root {
  overflow: hidden;
}
.topmost-container-on-same-element-as-css-vars {
  height: 100%;
  overflow: auto;
}

Then the container is scrolling instead and all scrollbars under the container can have var-styling.
My suggestions for theming on scrollbars is either the solution in my PR, or I also found these for dark-theme:
on *::-webkit-scrollbar-track: background: #202020
on *::-webkit-scrollbar-thumb: background: #3e3e3e
If you like these, they would need to be added... somewhere. I'm shabby with scss, didn't know where to put it. But I think the values in the PR are also ok.