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Could you send us a simplified demo with the code you generate these labels with? It will make it easier for me to help because at the moment I'm not sure how you do it.
The example you sent is not entirely a good solution, it is limited and imprecise. Unfortunately, using the basic API settings it is not possible to show the seasons.
Due to the fact that there is no specific example with the seasons and it seems like a nice example so I spent more time and prepared a demo generating labels with seasons instead of years using SVGRenderer in the chart.event.render() callback function.