I'm running into this same issue and the link above didn't fix my problem with it showing in the systray. Has anybody found a solution?
EDIT: Scratch that. If I use a different theme (like the Ubuntu Community Theme), the icon doesn't pop up. If I switch back to the default Gnome theme, it works fine.
That sounds like it's likely the theme yeah. Right now that it works at all pretty much depends on an Ubuntu shell extension they used to keep AppIndicators working, but it makes sense that anything that follows Gnome a bit more closely ends up with the extension not working. It's not really that PIA doesn't pop the icon but rather that the theme doesn't place the indicators area at all.
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EDIT: Scratch that. If I use a different theme (like the Ubuntu Community Theme), the icon doesn't pop up. If I switch back to the default Gnome theme, it works fine.
This is the output I get when starting the run.sh script from a console: