Favicon and monochromatic vector logo for docs site

## Goal

Investigate options for a favicon for the docs site (and potentially Graph Explorer itself). The favicon should ideally be:

- Monochromatic and vector-based (SVG)
- Properly supporting light and dark mode

This exploration may also surface a stronger in-app logo for Graph Explorer.

## Expected Outcome

- A recommendation on favicon approach (format, sizes, light/dark handling — e.g. SVG with `prefers-color-scheme`, `` media queries, or theme-aware assets)
- One or more candidate designs / mockups
- An assessment of whether the favicon work should extend to a refreshed in-app Graph Explorer logo, with a follow-up task or epic if so
- Notes on how Starlight consumes favicons (`favicon` config, custom `` entries) so the docs site can adopt the result

## Related Issues

- Originated from #1754

> [!IMPORTANT]
> Internal only — this issue is maintained by the core team and is not accepting external contributions.

Start by reviewing the docs site's Starlight favicon configuration and the existing Graph Explorer branding. Compare the listed SVG and theme-aware approaches, prepare candidate designs or mockups, and document a recommendation plus whether the in-app logo needs a follow-up task or epic.

Written by the indexing model from the issue text.