To add a clickable button to a tooltip you should first make sure that correct options for the tooltip are used.
See the green highlight in the image attached.
- useHTML needs to be set to true to enable adding of HTML structures, like button
- pointerEvent in the tooltip's style needs to be set to "auto" to enable click events
Next, you could write the onclick functions for the button(s) as a string and use
- (highlighted in red) Highcharts related functions and access it's related objects. The function for formatter has access to JavaScript variables passed into the functions, so you could reference the related API reference for pure JS library.
- (highlighted in blue) general JavaScript, global functions and objects
For native Android callback to on click events for specific chart elements you could check the documentation section in the highcharts-android GitHub repository in here.