I have a very similar setup and the same problem. Interestingly enough, the problem goes away if I configure Monitor1 as "RightOf" instead as "LeftOf". Then the sddm greeter is on the primary screen, and the other one stays black.
$ cat /etc/X11/xorg.conf --- snip --- Section "Monitor" Identifier "Monitor0" VendorName "HP" ModelName "w19" HorizSync 30.0 - 83.0 VertRefresh 55.0 - 75.0 Option "DPMS" Option "Primary" EndSection Section "Monitor" Identifier "Monitor1" VendorName "Dell" ModelName "P190S" HorizSync 30.0 - 81.0 VertRefresh 56.0 - 76.0 Option "DPMS" Option "RightOf" "Monitor0" # FIXME this should be: # Option "LeftOf" "Monitor0" Option "Rotate" "CW" EndSection Section "Device" Identifier "Device0" Driver "radeon" VendorName "Radeon" Option "AccelMethod" "XAA" Option "AccelDFS" "1" Option "EnablePageFlip" "1" Option "ColorTiling" "1" Option "Monitor-HDMI-0" "Monitor0" Option "Monitor-VGA-0" "Monitor1" EndSection Section "Screen" Identifier "Screen0" Device "Device0" Monitor "Monitor0" DefaultDepth 24 SubSection "Display" Depth 24 Virtual 2464 1440 EndSubSection EndSection / Knut Esztermann -- Linux - Less bugs for less bucks! text/html > /dev/null
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