chore: update dependencies and documentation for Vue example

[wassimoo]

• Updated @ory/client, @ory/client-fetch, and vue to their latest versions.
• Adjusted local development commands in documentation to reflect correct port configurations.
• Updated documentation references regarding API and application URLs.

Related Issue or Design Document

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 security@ory.com) 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

[unatasha8]

word change, otherwise LGTM