I would concentrate on this. It sounds like, libreoffice started but the window is not visible to you. I would stop “installing/reinstalling/removing” libreoffice.
Maybe:
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Main UI of all applications won't show all of a sudden - English - Ask LibreOffice
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If you alt-tab (task switcher), does it show up and is it selectable.
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Is there some indication (i.e., icon) that libreoffice is running from the KDE panel. Hover over the KDE panel. If there is, you can right-click, select More and select a window property like resize, maximize, etc.
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The below was probably a typo, but did you delete the contents of $HOME/.cache/ (notice the . in front of cache). Logoff/on after doing the remove.
- [Solved] LibreOffice Writer misbehaving / Applications & Desktop Environments / Arch Linux Forums
Note thewmctrl -r libreoffice -e 0,128,128,512,512
command.
This seems like a common issue, where libreoffice is running but the window is not visible for whatever reason.