Sidebar heading nav issues

Problem

The sidebar heading navigation (added in #2822) currently seems to have a few oddities:

1. Header items can be hard to differentiate from chapter items. In this case the user does not know where the headers end and chapters begin:
   
2. Chapters and headers have different spacing. In theory I like that but it's not enough of a difference to help with the UX. If that is adjusted, it'd probably be preferable to have less spacing between chapters than between headers.
3. There is an invisible <li><ol class="section"></ol></li> between each heading:
   Edit: Presumably resolved. Removed my example image.
4. All formatting of a header is kept - including images, videos, buttons, etc. This is not necessarily an issue but can look a bit odd in some cases:
   
5. The indicator dot can go off-screen. It would be nice if it would auto-scroll the sidebar to keep the dot on screen.

Steps

No response

Possible Solution(s)

No response

Notes

Tested on Windows 11 in the Zen Browser (based on Firefox 142.0.1).
Overall I really like this feature and it will likely replace mdBook-pagetoc for us.

Version

mdbook v0.5.0-alpha.1

Start from the sidebar heading navigation introduced in #2822 and reproduce the reported behavior in mdBook v0.5.0-alpha.1 using the screenshots and listed cases. Inspect the navigation markup and styling, then verify clearer header/chapter separation, appropriate header formatting, and indicator-dot scrolling without regressions.