I had the same problem on Plasma 6. The solution is to create a custom setting in System Settings >> Window Management >> Window Rules. For the record, I start Conky with a script so you will have to adapt your rule for your situation.
Rule name: Conky
Description: Conky
Window class (application) - Exact Match - Conky
Match whole window class: No
Window types: All selected
Virtual Desktop: Force - Desktop 1
Activities: Force - Default
Keep below other windows: Force - Yes
Skip taskbar: Force: Yes
No titlebar and fram: Force - Yes
Focus stealing prevention: Force - None
I should also add that this rule works when running Conky with
own_window_type = 'normal',
in your Conky configuration file.
I haven’t moved on to Wayland yet so your mileage may vary with this setup.
Anyway, are you using Wayland for any specific reason? If not, you still have the option of using x11 for now. Wayland is still not yet the standard and, as you are experiencing right now, it still has some kinks to iron out.
Another option (maybe) is to find out if there are Wayland-based conky alternatives.
I think that this may be fixed more quickly for x11 than for Wayland, but now it seems it may just be related to the whole Plasma 6 update in general.
Try installing Openbox and running Conky to see if the same issue occurs. Openbox is a small install (1250.45 KiB), and you can remove it right after. Just want to test if it’s Plasma6-specific or not.
PS: You can run any of your apps within Openbox without issue, including KDE system settings.