chore: update vercel ai gateway guide

[smakosh]

Summary by CodeRabbit

• Documentation
  • Updated migration guide with simplified code examples for provider setup and configuration
  • Refined documentation to focus on unified LLM Gateway integration approach
  • Streamlined guidance emphasizing automatic routing and caching capabilities
  • Removed comparative sections for a clearer migration path

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[coderabbitai]

Walkthrough

The migration documentation for transitioning from Vercel AI Gateway to LLM Gateway has been updated to emphasize a unified single-provider approach, removing comparative content and updating code examples accordingly.

Changes

Cohort / File(s)	Summary
Documentation - Migration Guide Update apps/ui/src/content/migrations/vercel-ai-gateway.md	Updated migration guidance to focus on unified LLM Gateway provider approach; removed introductory comparison section, replaced provider-specific imports with LLM Gateway setup, removed comparative table "Why Teams Switch to LLM Gateway", and removed "What Changes After Migration" section

Estimated code review effort

🎯 1 (Trivial) | ⏱️ ~3 minutes

Possibly related PRs

• docs: improve marketing copy across landing and docs #1485 — Modifies the same migration documentation to replace Vercel-specific provider usage with unified LLM Gateway provider configuration
• feat: add migration guides to landing page #1482 — Adds the migrations content collection and pages that host this documentation file

Suggested reviewers

• steebchen

🚥 Pre-merge checks | ✅ 3

✅ Passed checks (3 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The pull request title accurately describes the main change: updating documentation for the Vercel AI Gateway guide.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.

_{✏️ Tip: You can configure your own custom pre-merge checks in the settings.}

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