What this PR does

Before this PR:
Groq uses the OpenAI-compatible provider (type: 'openai'). In AI SDK v6, the OpenAI provider sends reasoning_content in assistant messages by default, which Groq's API rejects on multi-turn conversations.

After this PR:
Groq uses the dedicated @ai-sdk/groq provider, which properly handles Groq's message format and does not send unsupported fields like reasoning_content.

Fixes #12327

Why we need it and why it was done in this way

The following tradeoffs were made:
Added @ai-sdk/groq as a new dependency (~small bundle impact via dynamic import).

The following alternatives were considered:

• Stripping reasoning_content from messages before sending to Groq — fragile and would need to be maintained as message format evolves.
• Using the dedicated @ai-sdk/groq provider (chosen) — the SDK handles Groq's API format natively, consistent with how other providers (Anthropic, Google, DeepSeek, etc.) have dedicated packages.

Breaking changes

None.

Special notes for your reviewer

• Groq is registered as a dynamic provider in providerInitialization.ts (lazy-loaded), consistent with other non-core providers like Mistral, Cerebras, Perplexity.
• A static mapping groq: 'groq' is added in factory.ts to ensure the provider ID resolves to the dedicated provider instead of falling through to OpenAI compatible.

Checklist

• PR: The PR description is expressive enough and will help future contributors
• Code: Write code that humans can understand and Keep it simple
• Refactor: You have left the code cleaner than you found it (Boy Scout Rule)
• Upgrade: Impact of this change on upgrade flows was considered and addressed if required
• Documentation: N/A — internal provider routing change, no user-facing feature change.
• Self-review: I have reviewed my own code before requesting review from others

Release note

Fix Groq multi-turn conversation errors caused by unsupported `reasoning_content` field by switching to the dedicated `@ai-sdk/groq` provider.