feat(ai-gateway): Use Claude CLI with AI Gateway

[tomek-labuk]

Description

Fixes #issue

Preview Links

Here are the updated links:

How-tos:

• https://deploy-preview-3644--kongdeveloper.netlify.app/how-to/use-claude-code-with-ai-gateway-anthropic/
• https://deploy-preview-3644--kongdeveloper.netlify.app/how-to/use-claude-code-with-ai-gateway-azure/
• https://deploy-preview-3644--kongdeveloper.netlify.app/how-to/use-claude-code-with-ai-gateway-openai/
• https://deploy-preview-3644--kongdeveloper.netlify.app/how-to/use-claude-code-with-ai-gateway-gemini/
• https://deploy-preview-3644--kongdeveloper.netlify.app/how-to/use-claude-code-with-ai-gateway-bedrock/
• https://deploy-preview-3644--kongdeveloper.netlify.app/how-to/use-claude-code-with-ai-gateway-dashscope/
• https://deploy-preview-3644--kongdeveloper.netlify.app/how-to/use-claude-code-with-ai-gateway-huggingface/

AI Proxy examples:

• https://deploy-preview-3644--kongdeveloper.netlify.app/plugins/ai-proxy/examples/claude-code-vertex/
• https://deploy-preview-3644--kongdeveloper.netlify.app/plugins/ai-proxy/examples/claude-code-bedrock/
• https://deploy-preview-3644--kongdeveloper.netlify.app/plugins/ai-proxy/examples/claude-code-gemini/
• https://deploy-preview-3644--kongdeveloper.netlify.app/plugins/ai-proxy/examples/claude-code-openai/
• https://deploy-preview-3644--kongdeveloper.netlify.app/plugins/ai-proxy/examples/claude-code-anthropic/
• https://deploy-preview-3644--kongdeveloper.netlify.app/plugins/ai-proxy/examples/claude-code-dashscope/

AI Proxy Advanced examples:

• https://deploy-preview-3644--kongdeveloper.netlify.app/plugins/ai-proxy-advanced/examples/claude-code-vertex/
• https://deploy-preview-3644--kongdeveloper.netlify.app/plugins/ai-proxy-advanced/examples/claude-code-bedrock/
• https://deploy-preview-3644--kongdeveloper.netlify.app/plugins/ai-proxy-advanced/examples/claude-code-gemini/
• https://deploy-preview-3644--kongdeveloper.netlify.app/plugins/ai-proxy-advanced/examples/claude-code-openai/
• https://deploy-preview-3644--kongdeveloper.netlify.app/plugins/ai-proxy-advanced/examples/claude-code-anthropic/
• https://deploy-preview-3644--kongdeveloper.netlify.app/plugins/ai-proxy-advanced/examples/claude-code-dashscope/

Landing page:

• https://deploy-preview-3644--kongdeveloper.netlify.app/ai-gateway/ai-clis/

Checklist

• Tested how-to docs. If not, note why here.
• All pages contain metadata.
• Any new docs link to existing docs.
• All autogenerated instructions render correctly (API, decK, Konnect, Kong Manager).
• Style guide (capitalized gateway entities, placeholder URLs) implemented correctly.
• Every page has a description entry in frontmatter.
• Add new pages to the product documentation index (if applicable).

[netlify]

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[lmilan]

Left some suggestions, plus two issues:

• The OpenAI examples are missing
• The Gemini/Vertex credentials are not in 1Password so I couldn't test those. I tried using the examples here but had issues with the JSON