I installed QGIS 3.4 with the repository https://qgis.org/ubuntu-ltr bionic main on an Ubuntu 18.04 machine. I had some troubles due to the presence of several repositories listed in my file sources.list. But now the software is installed and is properly running.
However its settings are not stable : neither the toolbar's display nor the location of the panels nor the import of my personalized color palette nor even the recently opened project files nor the connection to the databases are kept by the software.
I checked if the profile folder existed : /home/user/.local/share/QGIS/QGIS3/profiles/default. It's here, no problem. It has even the correct writing accesses for the owner and its group (and is "read-only" for the other users).
Do you have some clues?