I have (I think) exactly the same problem: I get flickering pattern on my laptop display, but perfectly fine output through a monitor via HDMI.
I am using nvidia-driver-470 (470.86) and kernel 5.13.0-27-generic which was recently installed on my system (prior kernel was 5.11.0-46-generic - which functions correctly).
apt show --installed nvidia-driver* | grep "Version"
Version: 470.86-0ubuntu0.20.04.2
And these are the two graphics chipsets in my laptop:
lspci | grep "VGA"
01:00.0 VGA compatible controller: NVIDIA Corporation TU106 [GeForce RTX 2060] (rev a1)
05:00.0 VGA compatible controller: Advanced Micro Devices, Inc. [AMD/ATI] Renoir (rev c5)
The other versions of the nvidia proprietary driver that are available via Software & Updates (460, 495) fail in the same fashion.
nvidia-bug-report.log.gz (284.9 KB)
This is an example of what I see on my laptop screen (no external monitor attached in photo):
I get similar errors reported via journalctl -p 3 -r -b however these errors are also present if I use the 5.11.0-46 for which both displays work correctly.
Jan 22 14:12:55 ... kernel: [drm:nv_drm_master_set [nvidia_drm]] *ERROR* [nvidia-drm] [GPU ID 0x00000100] Failed to grab modeset ownership
Jan 22 14:12:55 ... kernel: [drm:nv_drm_master_set [nvidia_drm]] *ERROR* [nvidia-drm] [GPU ID 0x00000100] Failed to grab modeset ownership
Jan 22 14:12:55 ... kernel: [drm:nv_drm_master_set [nvidia_drm]] *ERROR* [nvidia-drm] [GPU ID 0x00000100] Failed to grab modeset ownership
...
Jan 22 14:12:36 ... kernel: ucsi_ccg 2-0008: ucsi_ccg_init failed - -110
Jan 22 14:12:36 ... kernel: ucsi_ccg 2-0008: i2c_transfer failed -110
Jan 22 14:12:36 ... kernel: nvidia-gpu 0000:01:00.3: i2c timeout error e0000000
...