Created attachment 7141 screen capture (vertical) Please test (try) the whisker menu with vertical, rather thin (20 pixels) panel too. Experience is that the icon "disappears" (becomes a dot). Possibly because of the (left and right) padding of the icon.
Created attachment 7142 screen capture (horizontal)
The version is xfce4-whiskermenu-plugin 2.1.1-0ubuntu1 amd64
There is no absolute padding. *All* padding come from GTK. If you use a different theme (such as Greybird), or you switch to the GTK3 panel (which is still in development, true), then the icon is not a dot on a vertical 20px panel. There really isn't much I can do differently, sorry.
Please, at least give some idea, where to try to post this issue. Regarding the themes: there is no any change. In Appearance, changing either the "style" or the "icons" (icon set), the Whisker icon remains microscopical. All other icons resize good, only the whisker do not.
Did you restart the panel or log out and log back in after changing the theme? I have found that Whisker Menu does not properly change size until you do one of those things after switching themes. On my computer in Arch Linux, Greybird doesn't have the excess padding, so the icon is larger. The other icons are launchers on a GTK2 panel, so they are GTK2 buttons. Whisker Menu 2.1.1 is a GTK3 button, so it has larger padding. The extra padding is out of my control.
Graeme Gott referenced this bugreport in commit f8cfe65b6017768e1ad559b336b517c6e60d30c3 Fix excessive padding on panel button. (bug #13611) https://git.xfce.org/panel-plugins/xfce4-whiskermenu-plugin/commit?id=f8cfe65b6017768e1ad559b336b517c6e60d30c3
After investigating the source code of the GTK3 panel, I discovered that I actually can override the padding to fix this issue.
So I see that you fixed this issue that I started having when I moved from Xubuntu 16.04 to 18.04, but it looks like your fixes adjusted some undesirable hard limits on the icon size that I don't think were present in the GTK2 version. Specifically, it looks like your code clamps the icon size depending on the widget size. This breaks my setup, and probably some others too. I put x/ythickness at 0 on all panel widgets for GTK2, and now the equivalent fix isn't working here. I couldn't figure out why, but looking at that specific commit explained it for me. Here's what my panel looks like: https://imgur.com/UnIedHo If I use the GTK3 inspector, I can change the icon size and it looks fine. Other GTK3 panel widgets, like the status notifier, look fine too. I don't know what they do to set the icon size. I thought I could just rip out the icon size setting code entirely and have it work, but the icon is oversized if I do that, so I just hardcoded mine to be panel size - 2. It looks like the 4.13 path is to do it intelligently using a given API call, but Bionic doesn't have 4.13 or that API. That makes me wonder, how did it always "just work" in the GTK2 version, and now it doesn't anymore?