Document Fliplet.AI chatbot path and correct chat examples

[tonytlwu]

Product areas affected

Fliplet developer documentation and the V3 library manifest.

What does this PR do?

Adds chatbot to the Fliplet.AI capability metadata so Studio can discover the built-in API from an implicit chatbot request. Corrects the documented multi-turn chat and streaming examples to match the current fliplet-core runtime: app code must retain assistant replies, and ask() does not accept a per-call options object. Corrects the image generation reference to the current gpt-image-2 default and base64 response. Regenerates the published documentation indexes.

JIRA ticket

N/A

Result

The generated llms-v3-libraries.json lists chatbot under the preloaded Fliplet.AI entry. The multi-turn example uses Fliplet.AI.createCompletion({ messages }) without asking for a provider key.

Checklist

• Added automated test coverage as appropriate for this change; existing index generator tests pass (141/141).
• Ran the strict documentation index build.

Deployment instructions

Publish this documentation change before building or deploying the paired Studio PR. Studio's prebuild task fetches the live library manifest and would otherwise overwrite its new chatbot keyword with the older published version.

Author concerns

The runtime still does not add assistant replies to Fliplet.AI().ask() history. This PR documents the current behavior; it does not change the runtime.

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