If there is only times.json in the default profile, then you use another
profile. You can list the profiles and start any of them by executing in a
terminal:
$ abrowser -P
By the way, if you choose another profile or create a new one, does the
problem still exist?
~/.mozilla/abrowser/*/bookmarkbackups are backups. The current bookmarks are
actually in ~/.mozilla/abrowser/*/places.sqlite (a SQLite database).
If you have many of them, it could be a good idea to export them as json
files from the Library ("Show All Bookmarks") window.
It can also be
APT never touches anything in /home (including the personal settings).