I saw some similar ideas but I think my propose is quite different.
The window where tabs outliner runs is separate from main window. My monitor is 17" not wide screen. I cannot use it that way... Even on widescreen it takes a lot of space.
So at linux I coded a script that when the mouse is near the left edge of the screen and was already above normal chromium window, tabs outliner window is shown;
It runs each 0.1s;
When it moves away from that window and to above normal chromium window, the normal window it is shown (so tabs outliner window goes to behind it). Other windows of other applications are protected from that behavior.
EDIT: the script also detects a url was clicked on tabs ouliner and automatically activates the normal chromium window!
I think you may be able to use the "on top" window flag to do that trick that may work on all OSs, when the mouse reaches the left edge of normal chromium window! EDIT: Just toggle on top, and toggle back again so release its top towards other applications.
PS.: my script probably only works on linux, it is a bash script...
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