How can I stop the system from displaying error messages like the example below?

(eog:1257): Gtk-CRITICAL **: gtk_css_section_get_file: assertion `section != NULL' failed

(eog:1257): Gtk-CRITICAL **: gtk_css_section_get_end_position: assertion `section != NULL' failed

(eog:1257): Gtk-CRITICAL **: gtk_css_section_get_end_line: assertion `section != NULL' failed

(eog:1257): Gtk-WARNING **: Theme parsing error: <data>:1:0: Unknown value 'GTK_SHADOW_NONE' for enum type 'GtkShadowType'

what are you doing when these messages appear?

are you starting a Gnome app in Konsole? if so does the app run? does it run fine? if so then probably ignore the messages and use Krunner or Kmenu to start the app

if messages appear using sudo to start a gui app then DON'T, use kdesudo

moved to Workspace (from plasma)

Based upon the names Gtk is dropping in the messages, I would suggest changing your Gtk theme to stop these messages from being printed.