Add Vercel AI Gateway + Cartesia integration page

[31Carlton7]

Summary

Adds submissions/vercel-ai-gateway-cartesia.mdx: using Cartesia Sonic 3.5 TTS and Ink speech-to-text through Vercel AI Gateway with the AI SDK — plain cartesia/<model> strings, one ai package dependency, one API key.

Draft status — do not review yet

The Cartesia models are built and certified in AI Gateway but not yet published in the public catalog (launch timing is being coordinated between Vercel and Cartesia). The quick start will be publicly runnable on launch day; I'll re-verify last_verified, confirm both examples against production, and mark this ready for review then.

Self-review

• Checked against the SKILL.md checklist (template conformance, style guide, scope)
• node scripts/update-docs-json.mjs run; --check and git diff --check pass
• Rendered page inspected locally with mint dev
• Model IDs cross-checked against docs.cartesia.ai/llms.txt (sonic-3.5, ink-whisper, ink-2)
• AI SDK usage verified against ai@7 (generateSpeech, transcribe, plain-string gateway routing) — TTS→STT round trip executed locally with exact transcript match

🤖 Generated with Claude Code

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Note

Low Risk
Documentation-only changes with no application or API code; low risk unless published before models are in the public AI Gateway catalog (noted as draft in the PR).

Overview
Adds a new community integration doc at submissions/vercel-ai-gateway-cartesia.mdx for routing Cartesia Sonic TTS and Ink STT through Vercel AI Gateway via the AI SDK (ai package), using cartesia/<model> strings and a single AI_GATEWAY_API_KEY.

The page includes prerequisites, a TTS→STT quick start (generateSpeech with cartesia/sonic-3.5, transcribe with cartesia/ink-whisper), notes on Ink 2 streaming and observability, and resource links. docs.json navigation is updated to include the new submission (along with other submission entries in the same diff).

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