Hi Alex! As far as I know (and others may please feel free to correct me), there's no way to do this in one sheet. There's a trick you can do with forcing a measure to be discrete and adding it as if it were a dimension, but that doesn't work when you use Measure Names/Values.
However, you might be able to do this in a dashboard by creating a separate sheet with the same structure, but with text instead of bars. Then, you could just fit that right under the bars sheet in the dashboard and hide the true labels and other elements to make the second sheet look like labels.
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Have you tried using reference lines? I have done this in a few bar charts where I wanted to show the measure, but I couldn't get the label to set individually for each bar. I created a reference line that was applicable to each bar, and asked the reference line to show the label. Then it worked how I wanted it to. Make sense?
Yes this is my best guess, i have been working on trying to do this thanks for confirming this is the best option
If all you want to do is add labels to the top of the bar (and not change the axis labels), then you don't have to use reference lines. You can just drop [Measure Names] onto the Label mark.