feat: add Vue 3 and Nuxt integration packages

[Jorgagu]

This PR adds Vue 3 and Nuxt integration packages for Ory Elements, bringing feature parity with the existing React/Next.js implementation.

New Packages

@ory/elements-vue - Vue 3 component library for Ory authentication UIs

• Complete set of UI components for Login, Registration, Recovery, Verification, Settings, and Consent flows
• Vue 3 Composition API with <script setup> syntax
• Full TypeScript support with proper type inference
• Default theme with Tailwind CSS v4 styling
• Internationalization support (80+ locales)
• Session management via SessionProvider
• Customizable components through slot overrides
• Storybook setup for component development and documentation

@ory/nuxt - Nuxt 3/4 integration module

• Auto-imported composables: useOryLogin, useOryRegistration, useOryRecovery, useOryVerification, useOrySettings, useOrySession, useOryLogout, useOryFlowError
• Server-side proxy for secure cookie handling
• Auth middleware for route protection
• Environment-based SDK URL configuration (NUXT_PUBLIC_ORY_SDK_URL)
• SSR-compatible session hydration

Example Application

Complete Nuxt example app demonstrating all authentication flows at examples/nuxt-app.

Related Issue or Design Document

Fixes #581

Checklist

• I have read the contributing guidelines and signed the CLA.
• I have referenced an issue containing the design document if my change introduces a new feature.
• I have read the security policy.
• I confirm that this pull request does not address a security vulnerability.
  If this pull request addresses a security vulnerability,
  I confirm that I got approval (please contact [email protected]) from the maintainers to push the changes.
• I have added tests that prove my fix is effective or that my feature works.
• I have added the necessary documentation within the code base (if appropriate).

Further comments

The Vue/Nuxt packages follow the same architecture patterns as the React/Next.js implementation:

• Same component hierarchy and naming conventions
• Same context/provider architecture (using Vue's provide/inject)
• Same flow handling logic and state management
• Same theming system structure with customizable components
• Same utility functions and SDK helpers

All authentication methods are supported including password, passwordless (code), social login (OIDC), passkeys, WebAuthn, TOTP, and recovery codes.

This fixes the issue #581

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Latest commit: 1723f6e

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 55.79%. Comparing base (f3fad4d) to head (1723f6e).
⚠️ Report is 274 commits behind head on main.

Additional details and impacted files

@@             Coverage Diff             @@
##             main     #586       +/-   ##
===========================================
+ Coverage   42.43%   55.79%   +13.36%     
===========================================
  Files         136      173       +37     
  Lines        2008     3194     +1186     
  Branches      288      472      +184     
===========================================
+ Hits          852     1782      +930     
- Misses       1149     1344      +195     
- Partials        7       68       +61     

Components	Coverage Δ
@ory/elements-react	54.63% <ø> (+17.84%)	⬆️
@ory/nextjs	62.52% <ø> (-3.46%)	⬇️

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[Jorgagu]

Hi @jonas-jonas @aeneasr @vinckr, this PR is ready for review 🎉

👋 @Jannik-Hm @Saganic, could you please test this as well and let me know if I missed anything during my own testing?

[vinckr]

Hey @Jorgagu
awesome, thanks!
Will take a look with @jonas-jonas as soon as time permits.

to resolve the format CI, can you run make format on your branch?

🐝

[Jorgagu]

@vinckr thanks! I ran make format, but it also reformatted some files that weren’t changed in this PR.

[aeneasr]

Cool stuff man! Given the massive size of the PR I'm not sure how quickly we can review this. We also need to figure out a way to add this to our e2e test suite (currently not open sourced) to ensure the advertised functionality matches the requirements. We also need to figure out who will be responsible on the team for maintaining those SDKs going forward (e.g. when we introduce new features). May I ask which approach you took to transfer the react elements to vue and nuxt? It will help us speed up review.