How can I remap the Caps Lock key to be Shift Lock?

In Gnome, you can change Caps Lock beavior in Gnome-Tweak-tool, then Typing:

Unfortunately, due to a bug/misfeature, the descriptions are hardly readable (they are truncated too short). You should match that with the full descriptions in /usr/share/X11/xkb/rules/evdev.lst --- this seems the one you want:

 caps:shiftlock       Caps Lock toggles ShiftLock (affects all keys)

Just select a couple of them until you get what you want.

Yes, in KDE at least, this is easily configurable in the Keyboard system settings. Various options for mapping Caps Lock to Shift with locking are available: