Using vercel-mcp-adapter I've got a functional MCP server up and running as an api route under my next.js app at /api/mcp . Now I want to add a chat page in my next.js app at /app/chat that has access to the tools at /api/mcp.

However I have two problems:

1. The MCP server uses HTTPStreamable as the transport (default OOTB behaviour for vercel-mcp-adapter), but I don't see any way to make a client use HTTPStreamable as the transport - the only supported option appears to be sse.
2. I have some chunky tool definitions in /api/mcp/route.ts that define available tools and argument schemas. I don't see any obvious way of adapting these to the tools arg that eg streamText exposes:

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const result = streamText({
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    model: lmstudio('google/gemma-3-27b'),
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    messages: convertToModelMessages(messages),
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    maxRetries: 1,
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    tools: ???, /* how can I re-use my tool defs from /api/mcp/route.ts? */
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    stopWhen: stepCountIs(5),
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});

Am I missing something obvious? Why does the MCP adapter use a totally different transport mechanism to the full-size AI SDK's MCP client?