docs(examples): migrate deprecated streamText result helpers to standalone helpers

[gr2m]

Background

Follow-up to #14652, which deprecated the five streamText result methods that convert a result into other forms and added stateless standalone helpers in their place. That PR intentionally deferred migrating the existing examples/, content/docs/, and content/cookbook/ usages to keep the API change reviewable:

Migrate remaining usages of the deprecated methods in examples/ and content/docs/ + content/cookbook/ to the new standalone helpers. Intentionally deferred to a follow-up PR so the API change here stays reviewable.

This PR is that follow-up.

Summary

Migrated every remaining usage of the deprecated result methods to the standalone helpers exported from ai. The result object's .stream is passed to the helper directly:

Deprecated (on streamText result)	Standalone replacement
result.toUIMessageStream(opts)	toUIMessageStream({ stream: result.stream, ...opts })
result.toUIMessageStreamResponse(opts)	createUIMessageStreamResponse({ stream: toUIMessageStream({ stream: result.stream, ...streamOpts }), ...responseInit })
result.pipeUIMessageStreamToResponse(res, opts)	pipeUIMessageStreamToResponse({ response: res, stream: toUIMessageStream({ stream: result.stream, ...streamOpts }) })
result.toTextStreamResponse(init)	createTextStreamResponse({ stream: toTextStream({ stream: result.stream }), ...init })
result.pipeTextStreamToResponse(res, init)	pipeTextStreamToResponse({ response: res, stream: toTextStream({ stream: result.stream }), ...init })

For toUIMessageStreamResponse / pipeUIMessageStreamToResponse, the options object is split: stream options (originalMessages, generateMessageId, onFinish, messageMetadata, sendReasoning, sendSources, sendStart, sendFinish, onError) go into toUIMessageStream, while response-init options (headers, status, statusText, consumeSseStream) stay on the responder helper.

Scope: 149 files (80 examples, 37 docs, 32 cookbook).

Notable cases:

• agent.stream() results (content/cookbook/01-next/77-track-agent-token-usage.mdx) return a StreamTextResult, so their toUIMessageStreamResponse is the deprecated method and was migrated. Where the snippet used the <AgentUIMessage> generic to type the messageMetadata callback, the message generic moves to toUIMessageStream<ToolSet, AgentUIMessage>.
• streamText + Output routes (e.g. use-object, stream-object) use streamText, so their toTextStreamResponse is deprecated and was migrated. streamObject results — whose toTextStreamResponse/pipeTextStreamToResponse are not deprecated — were left untouched (none were present in the migrated files).
• Chunk iteration (examples/ai-functions/.../anthropic-reasoning-ui-stream.ts): the standalone toUIMessageStream returns a plain ReadableStream rather than the old AsyncIterableStream, so the for await was replaced with a reader loop.
• MDX highlight ranges: expanding single-line imports / one-line returns shifted line numbers inside fenced code blocks; affected highlight="..." attributes were recomputed.
• Minor correctness fix in 12-use-chat-an-error-occurred.mdx: the migrated snippet's stale getErrorMessage option was corrected to toUIMessageStream's actual onError option.

Manual Verification

• oxfmt + oxlint clean on all changed TS/TSX files.
• tsc --noEmit on the affected example packages (ai-functions, ai-e2e-next, express, hono, fastify, nest, node-http-server, angular, next, next-openai-pages, nuxt-openai, sveltekit-openai) shows no migration-related type errors. (Pre-existing, unrelated errors in ai-functions azure/xai web-search example files are not touched by this PR.)
• No production package code changed, so no changeset is required.

Checklist

• All commits are signed (PRs with unsigned commits cannot be merged)
• Tests have been added / updated (for bug fixes / features)
• Documentation has been added / updated (for bug fixes / features)
• A patch changeset for relevant packages has been added (for bug fixes / features - run pnpm changeset in the project root)
• I have reviewed this pull request (self-review)

Future Work

• Deduplicate workflow's toUIMessageChunk against the new ai helper (tracked in feat(ai): expose toUIMessageChunkStream helper #14652).
• Remove the five deprecated instance methods in the next major release (v8).

Related Issues

Follow-up to #14652.