The quickest and most readily available method is to use the ubuntu-drivers utility.
KDE does not have a tool for managing drivers, though individual distros do., as you saw.
Neon isn’t an actual full-on distro, BUT you can also install Kubuntu/Lubuntu’s GUI utility software-properties-qt. This will add the Software Sources tool to Discover’s settings, which also includes the Driver Manager.
The ubuntu-drivers command is a command line tool and while its easier to use then doing apt install and knowing what specific package you need to install - it is not much better and requires familiarity with the terminal and command line tools, as well as being open to reading and investigating - something that my latest Linux convertee is not.
The software-properties-qt application is slightly better - in that it is a GUI application and while it is not immediately obvious how to use it to install drivers - there are large inviting buttons to press and so its a useful solution, if not for some huge problems:
It is not pre-installed on Neon (at least the user edition).
It cannot be installed from Discover
After installing it manually (for example, using Synaptic), it does not show up in the main menu. It does install desktop entry files, so I don’t understand why it isn’t listed - but I also checked the files and even if these were visible - they will not work because they either don’t sudo or use lxqt-sudo that: isn’t installed by default; isn’t required as a dependency; can’t actually be installed on current Neon due to hard dependency on qtbase-abi-5-15-3 which isn’t available; does not work even on Plasma Wayland even if you manage to install it.
It should be runnable with pkexec, but it does not install a policy file so while it is possible to run it under Plasma Wayland, it is very hard to do so.
Best process I could find so far - Assuming Neon for Plasma 6.0 - is to install Synaptic and then either install software-properties-qt and then run pkexec env WAYLAND_DISPLAY=$WAYLAND_DISPLAY XDG_RUNTIME_DIR=$XDG_RUNTIME_DIR QT_QPA_PLATFORM=wayland software-properties-qt from the main menu or krunner; or just search for and install the relevant nvidia-driver-VERSION package using synaptic.
Yes, as it is Ubuntu’s software, not KDE’s . The Driver Manager has been a tab in the Software Sources tool for ages now, as opposed to a separate custom System Settings module like it used to be before it added support Lxqt/Lubuntu.
Ubuntu/Kubuntu/Lubuntu designed it to be launched from other applications, iirc - it is the Software Sources button that will now appear in Discover’s settings, for example. Or in Muon, if that still functions.
If you install the gtk variant software-properties-gtk, it will replace Synaptic’s basic repo management tool, so the driver manager can be accessed from there.
I don’t actually use the Software Sources tool, nor its driver manager, but I do have it installed on neon, to use as a reference and source for screenshots. I am semi-positive that I have used it in Plasma 6 (wayland, launched from within Discover) with no issue, but I can’t verify at the moment as those PCs are still packed for a move.
It is not - in Discover 6 (and IIRC it was like that even in the later 5 versions) the Settings page has the configuration for the sources implemented natively in Discover. There’s no external application.
I’m not sure what you mean by “Synaptic’s basic repo management tool” - I seem to recall that in the past there was an option from Synaptic to launch the software properties UI, but it does not seem to be there now - the only thing I could find was Settings → Repositories that just reloaded the repository list.
You can launch software-properties-gtk (after installing) by searching for “Software & Updates” in the main menu - which asks for a authorization when you launch it (it looks to have internal PolicyKit integration) but will only be satisfied by the password for root - which I don’t actually have set (or in any Ubuntu-style installation actually) so it cannot be used either.