This is great, thanks. I'll take a look when I get a chance this evening.

Do you mind adding some screenshots to your OP in the meantime, though?

Landing page without sidebar:

Reference page with sidebar:

Hamburger menu on emulated mobile device:

I just rendered and previewed everything locally. I really like the proposed changes; it feels like a clear improvement on top of what we already have.

I'm tempted to merge as-is, but two very minor thoughts first:

• While the highlighted "pink" colour looks good against the white background, it's a little garish for my tastes against the teal background. Is there perhaps a softer option that we could try? This is not a strongly held opinion, and you're the color expert, so feel free to go with your preferred aesthetic.
• One collateral benefit of moving everything to the navbar is that we "recover" a menu level. Along those lines, I can see that you already added a "Main functions" entry in the References section and I like this idea. Similarly, I wonder whether it makes sense to create a "Types" (or "Plot types") menu entry where can nest "Shapes", "Visualizations", and co. under? (Note: This is what we had originally, but we dropped it to avoid too-deep menu nesting... which may be moot now that the navbar has given us one menu level back.)

I had a sec, so actioned the second bullet point above. We can revisit the first later (maybe), but happy to merge now. These changes look fantastic, thanks @zeileis!

• I'll have a look at a better way to highlight the selected navbar link. Either by using a lighter color or by using a different type of highlighting. But I need some time to play with the CSS here.
• For my personal taste, the value added by the additional hierarchy level doesn't justify the additional click. So I would prefer the flatter menu. (Feel free to disagree, of course.)