Refactor tree controls into Vue

What does this MR do?

As part of the ongoing refactor of the repository tree view into Vue. This refactors some of the tree control buttons into Vue. Some of these links need the updated path in order to link to the correct place. This changes that by allowing them to react to the Vue Router route changes.

Closes #34794 (closed)

Screenshots

Does this MR meet the acceptance criteria?

Conformity

• Changelog entry
• Documentation created/updated or follow-up review issue created
• 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

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