Expose vue app instance for extensions

[cnotv]

Summary

Fixes #12628

Occurred changes and/or fixed issues

Logic already exists and exposing the Vue instance should not cause any harm.

Technical notes summary

Areas or cases that should be tested

Areas which could experience regressions

Screenshot/Video

Checklist

• [x] The PR is linked to an issue and the linked issue has a Milestone, or no issue is needed
• [x] The PR has a Milestone
• [x] The PR template has been filled out
• [x] The PR has been self reviewed
• [x] The PR has a reviewer assigned
• [x] The PR has automated tests or clear instructions for manual tests and the linked issue has appropriate QA labels, or tests are not needed
• [x] The PR has reviewed with UX and tested in light and dark mode, or there are no UX changes

[cnotv]

Closing due to blocking issues.