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Something like that should be possible to achieve in terms of chart assumptions, but the styling could be a bit hard to do, and would most likely require fair amount of work.
Here you can find Gantt demos, this should give you general idea what is possible to achieve: https://www.highcharts.com/demo/gantt
I noticed that in your example stages are shown on x axis, and date on y axis, so probably this demo should be what you are looking for:
Let me know if you have any further questions!