I'm trying out a brand new Debian 10 deployment on a cloud server, and there are two main problems:
1. KDE won't work in greater than VGA resolution over VNC (gray screen), even though I set 1920x1080 resolution in the console
2. I'm continually getting a "drkonqi closed unexpectedly" error in KDE ("Executable: drkonqi PID: 2508 Signal: Segmentation fault (11)")

Any ideas?

For #1, try turning off the Kscreen2 background service in KDE. I found that fixed my issues when running it in KVM, at least.

Please clarify some points:

What precisely do you mean by setting the resolution "in the console"?

What do you mean by not "greater than VGA resolution"?

Have you verified that the monitor is capable of 1920x1080? Is that resolution available in Plasma-->System Settings-->Hardware Display? (I know that KDE can display at that setting; I've used it myself.)

Same thing - no luck

1. The cloud server has a direct console connection (virtual KVM, since it's a VM). I changed the screen resolution there to 1920x1080, and it works fine from that connection.
2. Whoops, sorry - I meant XGA (1024x768). If I use XGA or lower in -geometry, KDE appears fine in VNC. Anything higher (1920x1080, for example) and I get a gray screen.
3. Yes, that's what the "console" resolution is set to (display "Virtual-1")

VNC server is tightvnc, and I'm launching it with "vncserver :1 -geometry 1920x1080 -localhost"

Would it be best to just reload the whole thing at this point? That should at least fix problem #2.