Nuxt fix server client

[rodriciru]

Summary
This PR introduces full support for isomorphic API clients within the Nuxt 3/4 ecosystem. Previously, the
@hey-api/client-nuxt was tightly coupled to Vue and could not be used inside Nitro server routes (/server/api/...).

This change enables the automatic generation and injection of a dedicated server-side client powered by
@hey-api/client-ofetch, allowing developers to use the same auto-imported SDK both in their .vue components and their
Nitro event handlers without any configuration overhead.

Fixes #1985 (#1985)

Key Changes

@hey-api/nuxt Module

• Dual Client Generation: The module now generates two separate clients into .nuxt/heyapi/client and
  .nuxt/heyapi/server.
• Nitro Integration: Automatically configures Nitro aliases so the same #hey-api import points to the Vue-friendly
  client on the frontend and the ofetch client on the server.
• Transpilation Fix: Moved generated output from node_modules/.cache to the root .nuxt folder to bypass Rollup's
  restriction on transpiling TypeScript files inside the node_modules tree, fixing the "Expected ',' got 'ident'"
  error in Nitro.
• Auto-imports: Registered auto-imports for the Nitro environment, enabling a seamless developer experience.

Ecosystem & Examples

• Nuxt 4 Support: Bumped internal module dependencies to support Nuxt 4 and Vite 6.
• Revamped Examples: Migrated the Nuxt example into a v3/v4 structure.
• Isomorphic Demo: Added a new Nitro route example (/server/api/pet/[id].get.ts) that uses the auto-imported SDK
  directly on the server.
• UI Improvements: Refined the demo dashboard with dynamic ID selection and comprehensive support for all Nuxt
  composables (useAsyncData, useFetch, etc.) while handling BigInt serialization correctly.

Testing

1. Run pnpm dev in the examples/openapi-ts-nuxt/v4 directory.
2. Verify that $fetch works in the browser.
3. Click "call /api/pet/:id (Nitro)" to verify the server-side SDK is correctly fetching data through the Nitro
   client.
4. Verify that all Nuxt reactive composables work without circular reference errors.

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[changeset-bot]

🦋 Changeset detected

Latest commit: 5c7fca9

The changes in this PR will be included in the next version bump.

This PR includes changesets to release 3 packages

Name	Type
@example/openapi-ts-nuxt-v3	Minor
@example/openapi-ts-nuxt-v4	Minor
@hey-api/nuxt	Minor

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 38.99%. Comparing base (bcdd174) to head (5c7fca9).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #3631   +/-   ##
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  Coverage   38.99%   38.99%           
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  Files         513      513           
  Lines       18771    18771           
  Branches     5565     5559    -6     
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  Hits         7319     7319           
  Misses       9255     9255           
  Partials     2197     2197           

Flag	Coverage Δ
unittests	38.99% <ø> (ø)

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commit: 5c7fca9

[rodriciru]

Please, tell me if the double client is acceptable or not!