Update assistant embed guide for Next.js example

[ethanpalm]

Documentation changes

Dependent on mintlify/assistant-embed-example#5

Closes https://linear.app/mintlify/issue/DOC-250/create-nextjs-version-of-assistant-embed-tutorial

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For Reviewers

When reviewing documentation PRs, please consider:

✅ Technical accuracy

• Code examples work as written
• Commands and configurations are correct
• Links resolve to the right destinations
• Prerequisites and requirements are accurate

✅ Clarity and completeness

• Instructions are clear and easy to follow
• Steps are in logical order
• Nothing important is missing
• Examples help illustrate the concepts

✅ User experience

• A new user could follow these docs successfully
• Common gotchas or edge cases are addressed
• Error messages or troubleshooting guidance is helpful

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Note

Low Risk
Documentation-only changes that adjust setup instructions and remove a descriptive section; no runtime or API behavior changes.

Overview
Updates the assistant-embed tutorial setup steps to support both Next.js and Vite versions of the example repo, adding a tool-selection step with separate install commands.

Removes the embedded “Project structure” section and makes minor wording/punctuation tweaks to step instructions for consistency.

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