Traditionally, one using a “from-scratch” Linux install might start in a console TTY and then use the startx command to start X.org and other applications alongside it (including the window manager like i3). This is often done through the .xinitrc file. In your case, it’s likely that you aren’t using such a method, and rather using a display manager (most likely sddm since you are using KDE Plasma) to launch your user session (a bit of an oversight on my part, my bad). When not having some kind of pre-launch file or some other service list to launch everything surrounding your desktop, you might have to rely on your window manager to ensure secondary processes are launched. I do believe sddm can be configured to allow for additional processes to be launched, but I’ll point you in the direction of doing it from i3’s config files as it’s quite simple to do.

Within your i3 config file, you can add exec entries into it. Typically exec entries are meant to be used with bindsym to launch things with a keybind, but you can use exec entries on their own line to launch applications when the configuration file is read (on startup). For instance, you could add the line exec --no-startup-id "/usr/lib/polkit-kde-authentication-agent-1 &" in order to launch KDE’s polkit authentication agent with your i3 instance, at which point applications (like SQL Workbench) should be able to make use of. As usual, changing your i3 config does require restarting your session for changes to take effect.