Use an instantiated vue object to reference $watch from for ESM compatibility

[rtibbles]

Summary

Description of the change(s) you made

• Instantiates a vue object in serverSync.js in order to use its $watch method

Manual verification steps performed

1. Ensured that no error occurred when first opening Studio, due to the $watch invocation
2. Ensured that a change subsequently synced upon making an edit

References

Fixes #4103

Contributor's Checklist

PR process:

• If this is an important user-facing change, PR or related issue the CHANGELOG label been added to this PR. Note: items with this label will be added to the CHANGELOG at a later time
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Studio-specifc:

• All user-facing strings are translated properly
• The notranslate class been added to elements that shouldn't be translated by Google Chrome's automatic translation feature (e.g. icons, user-generated text)
• All UI components are LTR and RTL compliant
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Reviewer's Checklist

This section is for reviewers to fill out.

• Automated test coverage is satisfactory
• PR is fully functional
• PR has been tested for accessibility regressions
• External dependency files were updated if necessary (yarn and pip)
• Documentation is updated
• Contributor is in AUTHORS.md

[bjester]

Lets try it out

[bjester]

No sentry errors, looks good