Sorry for the long post, it is needed to describe the whole picture.
I am on Majaro latest stable update, Obsidian is installed from the repo, not something like AppImage.
First of all the Obsidian icon was not displayed on its “window button” in the taskbar (i.e. “Window Buttons” plugin of xfce-panel). Instead, only some empty rectangle was rendered.
I figured out that it was Obsidian’s own fault for putting its app icon not in a proper freedesktop.org-compliant location of /usr/share/icons/hicolor/<size>/apps/ but only into a legacy location of /usr/share/pixmaps/.
The solution was to create an $XDG_DATA_HOME/icons/hicolor/<size>/apps/, copy the icon there, and run gtk-update-icon-cache. Since the icon size was 512, the <size> part of the path was 512x512.
This worked in the sense that after that the Obsidian icon appeared on its window button.
However, after that I noticed a new visual glitch. I use XFCE with the option “Cycle through windows in a list”. With this option on, when you switch windows with Alt-Tab the windows are displayed as a vertical list. In the list each item is a window name with the app icon on the left of the window name.
This is how it looked before I fixed the taskbar:
So the newly-appeared glitch: if an Obsidian window is open, then its icon on the left of its name has its (icon’s) full height of 512 pixels, which makes the row take nearly half of my screen height. And as long as an Obsidian window is open, the row of each other window has the same height, even though all other app icons have their normal size.
I have tried resizing the Obsidian icon and putting it in the respective-size named directory, but it has no effect: the icon in the window list still has the height of 512 pixels.