docs(ai-gateway): publish AI Gateway module reference

[sam-prais]

Summary

• The AI Gateway module (base44.aiGateway/base44.asServiceRole.aiGateway) had JSDoc from fix(ai-gateway): resolve gateway by app id in the path #226 but was never added to the docs pipeline whitelist, so it never appeared in the generated SDK reference.
• Add AiGatewayModule and AiGatewayConnection to types-to-expose.json, and add AiGatewayConnection to types-to-delete-after-processing.json (same pattern as DeleteResult/ImportResult: keep it inline in the connection() method's Returns accordion, without a redundant standalone/appended section).
• Rewrite the module JSDoc for reference quality:
  • Explain what an OpenAI-compatible client is inline (no external link needed).
  • Clarify the credit quota is shared across all app users, not per-user — if the app runs out of credits, the gateway stops working for everyone until reset.
  • Link to the current model alias list (InvokeLLM's model param) instead of hardcoding a list that will drift.
  • Split the growing intro into ## Models, ## Authentication Modes, and ## Billing and limits sections, matching the Agents/Auth/Functions module pages.
  • Added a second, simpler @example (plain OpenAI SDK call) ahead of the existing tool-loop agent example, per the "start simple" convention.

Test plan

• npm test — 180/180 passing
• npm run create-docs — verified the generated page has no duplicate AiGatewayConnection/Properties section and no stray standalone nav page
• Previewed locally via mint dev against the paired mintlify-docs branch

[claude]

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[github-actions]

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{
  "dependencies": {
    "@base44/sdk": "npm:@base44-preview/sdk@0.8.39-pr.231.0f61b59"
  }
}

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