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Unfortunately, the API does no allow to add buttons here yet. It seems that this is something that may be requested as a feature, which I decided to do on our GitHub repository: https://github.com/highcharts/highcharts/issues/20229
There you can expect updates and participate in possible discussion about it.
However, using API options you can add custom buttons instead, e.g. in the context menu, see the demo below.
I hope it was helpful!