Stacked on top of #603 (`create-chat-sdk`).
Refreshes the chat-sdk.dev homepage styling:
- Adds Geist typography utilities (`text-heading-*`, `text-copy-*`) and
applies them to the hero, section headings, and copy.
- Adds a grid-based layout (`home-grid.css`) with consistent guide lines
for the stats, supported-platforms, code, and integrations sections.
- Adds a tabbed code showcase for the Chat SDK Core section, with window
chrome, a Geist syntax theme, and
`bot.ts`/handlers/cards/streaming/tools/state/multi-platform snippets.
- Scopes inline-code styling and sets the dark-mode
`--ds-background-100`/`--ds-background-200` tokens so `background-100`
is the elevated surface.
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Co-authored-by: Ben Sabic <bensabic@users.noreply.github.com>