Fix group path biding in view file

What does this MR do?

This MR fixes a bug where the maven duplicated settings would not work on sub-groups, this is because we were not passing full_path to the vue app, but path

We are also adding a dedicated feature test to avoid this to happen again.

Note that this work is still behind feature flag and this bug has been found when enabling it on particular sub groups on production.

Feature flag rollout issue: #297371 (closed)

Screenshots (strongly suggested)

No visual changes

Does this MR meet the acceptance criteria?

Conformity

• [-] Changelog entry
• [-] Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides
• [-] Database guides
• [-] Separation of EE specific content

Availability and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• Tested in all supported browsers
• [-] Informed Infrastructure department of a default or new setting change, if applicable per definition of done

Security

If this MR contains changes to processing or storing of credentials or tokens, authorization and authentication methods and other items described in the security review guidelines:

• [-] Label as security and @ mention @gitlab-com/gl-security/appsec
• [-] The MR includes necessary changes to maintain consistency between UI, API, email, or other methods
• [-] Security reports checked/validated by a reviewer from the AppSec team

Related to #296895 (closed)