Update ChatGPT documentation

[balloob]

Proposed change

Fix some outdated content and links for the OpenAI conversation integration.

Type of change

• Spelling, grammar or other readability improvements (current branch).
• Adjusted missing or incorrect information in the current documentation (current branch).
• Added documentation for a new integration I'm adding to Home Assistant (next branch).
  • I've opened up a PR to add logos and icons in Brands repository.
• Added documentation for a new feature I'm adding to Home Assistant (next branch).
• Removed stale or deprecated documentation.

Additional information

• Link to parent pull request in the codebase:
• Link to parent pull request in the Brands repository:
• This PR fixes or closes issue: fixes #

Checklist

• This PR uses the correct branch, based on one of the following:
  • I made a change to the existing documentation and used the current branch.
  • I made a change that is related to an upcoming version of Home Assistant and used the next branch.
• The documentation follows the Home Assistant documentation standards.

[netlify]

✅ Deploy Preview for home-assistant-docs ready!

Name	Link
🔨 Latest commit	f475a30
🔍 Latest deploy log	https://app.netlify.com/projects/home-assistant-docs/deploys/69266c2b0ba91a00083fa865
😎 Deploy Preview	https://deploy-preview-41981--home-assistant-docs.netlify.app
📱 Preview on mobile	Toggle QR Code... Use your smartphone camera to open QR code link.

---

To edit notification comments on pull requests, go to your Netlify project configuration.

[Copilot]

Pull request overview

This PR updates the OpenAI conversation integration documentation to fix outdated content and links. The changes modernize the documentation by using more general references to OpenAI's models and pricing structure, making it more maintainable as OpenAI evolves its offerings.

• Updated model documentation link to point to the general models page rather than a specific GPT-4o page
• Broadened the web search tool availability description to "gpt-4o and newer models" instead of listing specific models
• Simplified search context description by removing specific model names and updating the pricing link