How old is this installation? When was it last updated? What are the specs of the computer (inxi -baz)?
What do you mean init 6 in a terminal? Did you try Ctrl-Alt-F3 while that screen was displayed, login, then run init 6? Init 6 would be expected to cause reboot. If Ctrl-Alt-Fn doesn't produce a response, try striking the E key at the Grub menu and appending 3 to the end of the wrapped line that starts with linu before proceeding with boot.
It looks like Plasma doesn't want to start. Is this from an automatic login, or from a login screen? Is this trying to start a Wayland session, or X11? Can you try the other with different result? Plasma on Wayland in 15.3 is pretty crude, and trouble on 15.4 too. If using SDDM, you might try switching to LightDM with sudo update-alternatives --config default-displaymanager.
If you can login from vtty3, you might find upgrading to 15.4 would fix this. 15.3 is no longer supported, and easily upgraded to 15.4, either online or off.
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