This issue has been ongoing for several years.

When I launch Inkscape, the right panel with palettes always opens at half the width of the screen, even if I minimize it to its smallest width before closing it.

Additionally, palette tabs do not collapse to icon size when they are active.

Screenshot

I'd check the preferences settings :

I somewhat solved this issue for me for Windows. Once I have my docking dialogs set up the way I want them, I simply make the dialogs-state-ex.ini file read only. 
The only issue is that the more dialogs you have opened, the longer it takes to load up inkscape. My understanding that this has been corrected in the future v1.5. 
Done the same with the preference file. 

Not sure if this will work with a different OS. 

> I'd check the preferences settings :

If i set:  Don't save windows geometry - issue still exists

1. Describe your OS (your computer's Operating System: Mac/Windows/Linux/etc. & version).
2. Describe if Inkscape was newly installed, or upgraded from an earlier version.
3. Describe the version of Inkscape and the installer you used (the file you downloaded from the web: .msi/.exe/.zip/appimage/other, PPA/Snap/Flatpak, dmg/other ). 
4. Describe any special hardware being used, like tablet/stylus, external drives or multiple monitors.
5. Describe any helper/assistive programs or keyboard modifiers (macros, languages, etc.).

Also describe the displays and settings in use.