Ubuntu 20.04.3 - Black Screen on startup

I have a classic problem of "Black Screen" when Ubuntu starts and I'm not able to fix it.

The problem:

• Without the "nomodeset" option in GRUB_CMDLINE_LINUX_DEFAULT, I have a blackscreen on the main monitor of my laptop, but HDMI monitor works.
• With the "nomodeset" option in GRUB_CMDLINE_LINUX_DEFAULT, I have a blackscreen on the HDMI monitor, but main monitor of my laptop works.

Using "nomodeset" is not a solution as it use a driver that does not support lot of things (like second screen)

Computer specifications:

• ProBook 450 G7
• Intel Core i5-10210U
• Intel UHD 620
• Ubuntu 20.04.3 (fresh install)

Result of some commands:

$ sudo lshw -c video
    description: VGA compatible controller
    produit: UHD Graphics
    fabricant: Intel Corporation
    identifiant matériel: 2
    information bus: pci@0000:00:02.0
    version: 02
    bits: 64 bits
    horloge: 33MHz
    fonctionnalités: pciexpress msi pm vga_controller bus_master cap_list rom
    configuration : driver=i915 latency=0
    ressources : irq:149 mémoire:f0000000-f0ffffff mémoire:e0000000-efffffff portE/S:4000(taille=64) mémoire:c0000-dffff

$ lspci -nnk | egrep -iA3 "VGA" 00:02.0 VGA compatible controller
     [0300]: Intel Corporation UHD Graphics [8086:9b41] (rev 02)
     DeviceName: Onboard IGD    Subsystem: Hewlett-Packard Company UHD
     Graphics [103c:86a0]   Kernel driver in use: i915

$ sudo ubuntu-drivers autoinstall
No drivers found for installation.

$ xrandr
Screen 0: minimum 320 x 200, current 1920 x 1080, maximum 16384 x 16384
eDP-1 connected 1920x1080+0+0 (normal left inverted right x axis y axis) 344mm x 194mm
   1920x1080     59.98*+  59.97    59.96    59.93    39.98  
   1680x1050     59.95    59.88  
   1600x1024     60.17  
   1400x1050     59.98  
   1600x900      59.99    59.94    59.95    59.82  
   1280x1024     60.02  
   1440x900      59.89  
   1400x900      59.96    59.88  
   1280x960      60.00  
   1440x810      60.00    59.97  
   1368x768      59.88    59.85  
   1360x768      59.80    59.96  
   1280x800      59.99    59.97    59.81    59.91  
   1152x864      60.00  
   1280x720      60.00    59.99    59.86    59.74  
   1024x768      60.04    60.00  
   960x720       60.00  
   928x696       60.05  
   896x672       60.01  
   1024x576      59.95    59.96    59.90    59.82  
   960x600       59.93    60.00  
   960x540       59.96    59.99    59.63    59.82  
   800x600       60.00    60.32    56.25  
   840x525       60.01    59.88  
   864x486       59.92    59.57  
   800x512       60.17  
   700x525       59.98  
   800x450       59.95    59.82  
   640x512       60.02  
   720x450       59.89  
   700x450       59.96    59.88  
   640x480       60.00    59.94  
   720x405       59.51    58.99  
   684x384       59.88    59.85  
   680x384       59.80    59.96  
   640x400       59.88    59.98  
   576x432       60.06  
   640x360       59.86    59.83    59.84    59.32  
   512x384       60.00  
   512x288       60.00    59.92  
   480x270       59.63    59.82  
   400x300       60.32    56.34  
   432x243       59.92    59.57  
   320x240       60.05  
   360x202       59.51    59.13  
   320x180       59.84    59.32  
HDMI-1 connected primary 1920x1080+0+0 (normal left inverted right x axis y axis) 531mm x 299mm
   1920x1080     60.00 +  74.97*   50.00    59.94  
   1920x1080i    60.00    50.00    59.94  
   1600x1200     60.00  
   1680x1050     59.88  
   1280x1024     75.02    60.02  
   1440x900      59.90  
   1280x960      60.00  
   1152x864      75.00  
   1280x720      60.00    50.00    59.94  
   1024x768      75.03    60.00  
   832x624       74.55  
   800x600       75.00    60.32  
   720x576       50.00  
   720x576i      50.00  
   720x480       60.00    59.94  
   720x480i      60.00    59.94  
   640x480       75.00    60.00    59.94  
   720x400       70.08  
DP-1 disconnected (normal left inverted right x axis y axis)
HDMI-2 disconnected (normal left inverted right x axis y axis)

BONUS: When the computer goes into power saving, blackscreen after this and I have to force poweroff.

Did you know how to solve this problem ?

Thanks