Today I felt like I need to once again try this and have it fixed myself. My findings are as follows:
This is the only way it worked for me. Adding lines to ~/.bashrc, ~/.zshrc and ~/.config/fish made no effect.
So, a working route for me was adding
export SSH_ASKPASS=/usr/bin/ksshaskpass
export SSH_AUTH_SOCK="$XDG_RUNTIME_DIR"/ssh-agent.socket
to /etc/profile.d/ssh-askpass.sh
Another hiccup. Under no circumstances it worked as an auto-generated systemd service, failing each time and always. I made it work only with full path to the key of interest and without “< /dev/null” part. Neither tilde dash nor $HOME could be accepted in the path to ssh key.
And finally I have no prompt for the key password in Plasma - something I have had in Gnome by default since forever. Pity we have to jump so many hoops to get here but anyway it was well worth it.