`feat(ai-elements): add support for Base UI version of shadcn/ui`

Summary

Currently, @vercel/ai-elements assumes a Radix-based setup for shadcn/ui primitives. Projects that have adopted or migrated to the Base UI edition of shadcn/ui face component/type mismatches and peer dependency conflicts when initializing or importing AI Elements.

Problem

• The generated or copied components rely on @radix-ui/* primitives, while Base UI-based shadcn/ui projects use @base-ui-components/react.
• Attempting to run npx ai-elements in a Base UI environment breaks design consistency and forces developers to pull in heavy, redundant Radix dependencies alongside Base UI.

Proposed Solution

• Provide a CLI flag/option during setup (e.g., npx ai-elements --style base-ui or a prompt asking for the underlying primitive choice).
• Export Base UI-compatible variant primitives for components like PromptInput, Conversation, Message, and tool call dialogs/popovers.

Environment

• Framework: Next.js (App Router)
• UI Libraries: @base-ui-components/react, shadcn/ui (Base UI version), tailwindcss (v4)
• Package: @vercel/ai-elements

Start by tracing the ai-elements CLI setup flow and the component exports for PromptInput, Conversation, Message, and tool call dialogs or popovers. Compare their Radix assumptions with the Base UI environment described in the issue, then define how setup selects the primitive set and verify initialization and imports without requiring redundant Radix dependencies.