I upgraded from Fedora 38 to Fedora 39 on an AMD Ryzen 5 5600
with Nvidia Geforce RTX 3050 graphics card.  I'm running KDE
Plasma-X11, not Wayland.

I tried to install the GPU drivers several ways using repos/RPMs,
but was not successful.  I am using the Nvidia proprietary
drivers.  They support dual monitors with no problems; I've had
problems with the nouveau driver and dual monitors in the past.

I start the system in multi-user (CLI) mode and then run "startx"
to start X11 and Plasma.  (I started doing this in F38 because of
sddm hanging, which I was not able to resolve.)

When I log in with my user account and run startx, I get a black
screen (extending across both monitors) with an X cursor.  The
cursor moves in response to the mouse, but neither left or right
mouse button do anything. I can get to an alternate console
using alt-F3 and kill the login.

I have discovered a bit of a rain dance to get a working system.  I
can log in as root, run startx, and get a working KDE Plasma-X11
screen.  Then I log out to the sddm screen and log in again with
my user account.  After this, everything (or almost everything)
works correctly.

I've checked the system logs and the Xorg log for any error
or warning messages, but nothing looks incorrect or at all
informative.

Does anyone have any suggestions or insights into this problem?

I recommend using the rpmfusion vuild of the nvidia drivers.