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What a cool looking design!
You've discovered that a PNG with transparency nevertheless grabs input across the range of the image, even the transparent pixels. This is unlikely to change (in my uninformed opinion), because it would be near-impossible to implement in a web browser context (for Tableau Server, Tableau Online and Tableau Public).
I tried an exercise wherein I created a copy of your bar chart and then stripped out all of the colors, lines, and borders, and set the Worksheet shading to "None". My thought was to place this on top of the bottle image, so it would drive the interactive behaviors (the "tooltip chart") while the bottom-most sheet drove the actual bar colors and labels (the "bar chart"). This technique would rely on the top-most worksheet having a transparent background. However, that's not as easy as I had hoped.
It turns out that setting the Worksheet shading to "none" doesn't actually mean "transparent"; it just defaults to white.
I tried a trick that Shawn Wallwork demonstrated in this thread: Re: hide worksheet background. This trick uses a Map image to show something behind a chart. This would have allowed me to incorporate the bottle shape into the "tooltip chart", and maybe the transparency of the Map background would show the "bar chart" underneat. However, it turns out that the Map background image does not override the worksheet's default white color; the default white still shows through underneath, so when placed on the dashboard, the worksheet is still full opaque.
I was unable to find a method to get a worksheet to be truly transparent, in order to get my trick to work. It turns out there are a couple of Ideas open on the topic of worksheet transparency, and you may want to upvote them.
https://community.tableau.com/ideas/5466 (might end up getting rolled into 1692, but cast your vote anyway!)
In the meantime, I was unable to find a way to achieve the beautiful bottle shape while still having all the interactive behavior of the underlying bar chart. So sorry!
Here's an alternative design. It's not quite as nice as your original approach, but perhaps it will give you more ideas. Interactivity is restricted to the chart on the right side, but the bars extend over the image. See attached workbook.
Craft Beer Tableau v2.twbx 62.8 KB