score:1
Currently sunburst doesn't support data labels with connectors.
Share the idea of adding them to Highcharts here if you like: https://highcharts.uservoice.com/forums/55896-highcharts-javascript-api
You can create your own connectors functionality using SVGRenderer (first check whether the label appeared or not and draw a connector if needed) or you can try to adjust the functionality implemented for pie series to your case (overwriting sunburst core functions).
API reference: https://api.highcharts.com/class-reference/Highcharts.SVGRenderer
Code reference: https://github.com/highcharts/highcharts/blob/master/js/parts/PieSeries.js
Docs reference: https://www.highcharts.com/docs/extending-highcharts/extending-highcharts
Source: stackoverflow.com
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