docs: redesign landing hero, header, and footer

[Lucasgvdii]

Rework the docs site chrome into a Drizzle-inspired landing while keeping the Tungsten/V5 visual identity.

Hero & landing

• Split hero: punchy headline + tagline, "BACKED BY ObsessionDB" credit, TypeScript / Python (coming soon) badges linking to npm / PyPI, and a 2x2 action card grid under a "What you will find here" label.
• "Compatible with" provider strip (ObsessionDB, ClickHouse Cloud, Altinity, self-hosted, and any other ClickHouse) in a theme-aware, content-width band with centered, logo'd chips.
• Drop the prev/next pagination and section separators on the splash page.

Header

• Brand wordmark "ch-kit" in the self-hosted Goldman face, with a small "Docs" badge on non-landing pages.
• Centered "Home / Documentation" nav (mono caps); search, GitHub badge, and a single light/dark toggle (replacing the dropdown) on the right.
• Landing-only mobile hamburger (no-JS
  Details

  ) so the collapsed nav is reachable where Starlight renders no sidebar menu button.

Footer

• Site-wide footer: brand + tagline + social (GitHub real, Discord/X placeholder) and Documentation / Ports link columns. The dev-only Agentation overlay is gated to import.meta.env.DEV so prod drops it.

Misc

• Self-host Goldman; add provider logos; remove the "Introduction" sidebar entry; align the header logo flush to the shell gutter.