Correction: the SELinux issue appears to be unrelated; it's now happening on the older kernel as well.
However, the monitor issue is definitely related to kernel 5.11. I tried both kernel-core-5.11.1-300.fc34.x86_64 and kernel-core-5.11.0-156.fc34.x86_64 and had the same problem. Presumably this is related to the Intel graphics:
00:02.0 VGA compatible controller: Intel Corporation WhiskeyLake-U GT2 [UHD Graphics 620] (rev 02)
When I boot to this kernel, my system ends up using an entire CPU reporting SELinux failures around dbus-daemon (mostly having to do with flatpaks). It also can no longer display to my external monitor.
Booting to kernel-5.10.16-200.fc33.x86_64 (on the F34 userspace) fixes both issues.