docs: document the Ask AI chat widget's bottom prompt trigger

[devin-ai-integration]

Summary

Documents trigger="prompt", added to @fern-api/search-widget's AskAiChat in fern-platform#14238. Hold merge until @fern-api/search-widget@0.5.3 is published — the prop doesn't exist in 0.5.2, the current latest.

The prop's union widens, so every place that enumerated the modes had to be updated:

-<ParamField path="trigger" type="'floating' | 'inline' | 'none'" default="floating">
+<ParamField path="trigger" type="'floating' | 'prompt' | 'inline' | 'none'" default="floating">

plus the page description, the "Match the chat to your product" step, and AskAiChat.Prompt in the compound-component list.

The mode's behavior lives in the trigger ParamField rather than its own section, with the placement caveat also noted on placement. No changelog entry.

Vale is clean.

Link to Devin session: https://app.devin.ai/sessions/125e368fdff7447a9697b8e0dc265a7c
Open in Devin Desktop: https://app.devin.ai/desktop/session/125e368fdff7447a9697b8e0dc265a7c?variant=devin

[devin-ai-integration]

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[github-actions]

🌿 Preview your docs: https://fern-preview-devin-1787928035-ask-ai-prompt-docs.docs.buildwithfern.com/learn

Here are the markdown pages you've updated:

• learn/docs/ai-features/ask-fern/search-widget/ask-ai-chat