Angular - Fixing the cookie language provider to set proper cookie path

[sumeyyeKurtulus]

Description

Resolves #25858

Checklist

• I fully tested it as developer / designer and created unit / integration tests
• I documented it (or no need to document or I will create a separate documentation issue)

How to test it?

• You can switch to this branch for testing test/issue-25858
• Run this command yarn copy-to:app under npm > ng-packs
• Use this application for tests templates > app

Verify the bug is fixed

1. Open DevTools → Application → Cookies → http://localhost:4200
2. Delete .AspNetCore.Culture if it exists
3. Change the UI language
4. Check .AspNetCore.Culture:
   • Expected: Path=/
   • Wrong (old behavior): Path=/web
5. Open DevTools → Network
6. Trigger an API call (refresh or open a page that loads data)
7. Select a request to http://localhost:4200/api/...
8. Inspect Request Headers → Cookie
   • Expected: includes .AspNetCore.Culture=...
   • Wrong (old behavior): .AspNetCore.Culture missing