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I am trying to calculate two zonal statistics: count and variety.
My raster is a produce of r.raster.area with 4399 groups of pixels within a matrix of no-data values (which are coded as 65535).

My vector layer holds seven hand created polygons, which I have checked for validity, both with the built-in Validity Check algorithm and visually.
As I need Variety, the only tool I can use is the QGIS Zonal statistics tool in the Processing Toolbox. When I run the analysis, I get correct values for Count, but Variety is always 0 (which is impossible, as all the polygons hold many different values).

Could this be a problem with the high number of unique values (4399)?

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    I suspect this is a bug. When you need Variety measure, will you also select either Minority or Majority, or both of them along with Variety? – Kazuhito Nov 19 '20 at 4:54
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    Together with minority and majority I get a value for variety !=0, without 0. – Jochen Schwarze Nov 19 '20 at 10:21
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You need to also either Minority or Majority when asking for Variety, as pointed out by @Kazuhito and @Jochen Schwarze. It works smoothly when done so.

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