Add Vercel AI Gateway provider

[joshualipman123]

Summary

This PR adds support for Vercel AI Gateway as a provider, enabling users to access multiple AI models through Vercel's unified gateway interface.

Usage Example

from pydantic_ai import Agent
from pydantic_ai.models.openai import OpenAIModel
from pydantic_ai.providers.vercel import VercelAIGatewayProvider

# Uses environment variable automatically
model = OpenAIModel(
    'anthropic/claude-4-sonnet',
    provider=VercelAIGatewayProvider(),
)
agent = Agent(model)

# Or pass the API key directly
model = OpenAIModel(
    'anthropic/claude-4-sonnet',
    provider=VercelAIGatewayProvider(api_key='your-vercel-ai-gateway-api-key'),
)
agent = Agent(model)

[hyperlint-ai]

PR Change Summary

Added support for Vercel AI Gateway as a provider, enhancing access to multiple AI models through a unified interface.

• Introduced Vercel AI Gateway Provider for accessing AI models
• Updated documentation to include usage examples for the new provider
• Added instructions for setting up API keys and OIDC tokens

Modified Files

• docs/api/providers.md
• docs/models/index.md
• docs/models/openai.md

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[joshualipman123]

Hey @Kludex @DouweM! I'm an intern at Vercel and have been working on this PR to add support for our AI Gateway as a provider in Pydantic AI. Happy to discuss or answer any questions as helpful!

[DouweM]

@joshualipman123 Thank Joshua, looks good! Can you please resolve the conflicts and the suggestions I made? I also recommend running make format before pushing so we don't run into linter errors in CI.

[DouweM]

@joshualipman123 FYI, if #2283 merges before this, we'll need to update OpenAIModel in the docs to OpenAIChatCompletionsModel.

[DouweM]

@joshualipman123 Thanks Josh! I changed to the full name (Vercel AI Gateway) in docs, should merge when CI goes green :)