feat: Refactor Angular client integration and enhance error handling

[max-scopp]

• Updated openapi-ts.config.ts to configure Angular client plugin with error handling option.
• Modified app.component.html to use a demo component for displaying pet information.
• Refactored app.component.ts to remove direct API calls and integrate with the new demo component.
• Enhanced app.config.ts to provide the Hey API client for dependency injection.
• Improved error handling in client utilities and response processing.
• Added new demo component with HTML and CSS for displaying pet information and error messages.
• Updated client generation scripts to support new error handling and response structures.
• Refactored HTTP client usage to support custom injectors and improved error response handling.

[bolt-new-by-stackblitz]

Run & review this pull request in StackBlitz Codeflow.

[changeset-bot]

⚠️ No Changeset found

Latest commit: 2996bde

Merging this PR will not cause a version bump for any packages. If these changes should not result in a new version, you're good to go. If these changes should result in a version bump, you need to add a changeset.

This PR includes no changesets

When changesets are added to this PR, you'll see the packages that this PR includes changesets for and the associated semver types

Click here to learn what changesets are, and how to add one.

Click here if you're a maintainer who wants to add a changeset to this PR

[vercel]

@max-scopp is attempting to deploy a commit to the Hey API Team on Vercel.

A member of the Team first needs to authorize it.

[codecov]

Codecov Report

❌ Patch coverage is 23.07692% with 50 lines in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (main@275f403). Learn more about missing BASE report.
⚠️ Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
...c/plugins/@hey-api/client-angular/bundle/client.ts	2.63%	37 Missing ⚠️
...rc/plugins/@hey-api/client-angular/bundle/utils.ts	51.85%	13 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2422   +/-   ##
=======================================
  Coverage        ?   22.75%           
=======================================
  Files           ?      334           
  Lines           ?    32972           
  Branches        ?     1302           
=======================================
  Hits            ?     7503           
  Misses          ?    25460           
  Partials        ?        9           

Flag	Coverage Δ
unittests	22.75% <23.07%> (?)

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.

[max-scopp]

Closed in favour in pipeline fixes already done in #2423