This error is because you have virtualbox and kvm installed. The kernel modules conflict.

The "simple" solution is to use one or the other, but not both. You can, however, use both as long as you are willing to manually (or script) loading / unloading the kernel modules.

To see your modules

#Virtualbox modules
sudo lsmod | grep vbox

#kvm
sudo lsmod| grep kvm

To remove a module

# remove virtualbox
sudo rmmod vboxdrv
sudo rmmod vboxnetflt

#remove kvm
sudo rmmod kvm
sudo rmmod kvm_amd

use insmod

sudo insmod /full/path/to/your/modules

You can find the module with

locate kvm | grep .ko
locate vbox | grep .ko

Use the modules for your current kernel.

In version 6.12 of the Linux kernel, kvm module initialisation was changed — it now takes place as soon as the modules are loaded, and not the first time they are used. This prevents VirtualBox from working, as you discovered. This is documented in the VirtualBox 7.1.4 release notes. Since your system was upgraded from 6.11 to 6.14, that explains the sudden appearance of the symptoms.

To return to the previous situation (where KVM modules can be loaded without preventing VirtualBox from working), you can add kvm.enable_virt_at_load=0 to the kernel boot parameters. If you’re using Grub on a Debian derivative, that’s done by adding the parameter to the GRUB_CMDLINE_LINUX_DEFAULT= line in /etc/default/grub, then running sudo update-grub. After a reboot, this will allow VirtualBox to work, without preventing any other KVM-based tool from working either.

The other option is to disable the KVM modules entirely; this is safe, but will prevent any KVM-based tool from working. See cas’ answer for details.

Starting with the Linux 6.12 kernel, the behavior of KVM kernel modules has changed.

They now accept virtualization directly upon module load; this procedure was integrated without prior discussion some time ago.

Since this modification, kernels initialize virtualization upon module load by default, which causes VirtualBox VMs to fail to start.

To avoid this, you need to add the following line to the command line of the kernel in use:

kvm.enable_virt_at_load=0

To do this, edit the /etc/default/grub file.

sudo nano /etc/default/grub

Add kvm.enable_virt_at_load=0 to the line beginning with GRUB_CMDLINE_LINUX

Alternatively, you can create a custom file named /etc/default/grub.d/custom.cfg with this content:

GRUB_CMDLINE_LINUX="$GRUB_CMDLINE_LINUX kvm.enable_virt_at_load=0"

After saving the file with Ctrl + O and closing nano with Ctrl + X, run

sudo update-grub
sudo reboot

Execute this:

$ VBoxManage modifyvm <VirtualMachineName> --nested-hw-virt on

I finally found the answer. Even if Hyper-v was disabled in the Windows features, the service named HV Host Service was still running. I disabled all the Hyper-v services and now the option VT-x / AMD-V in the Vbox VM setting isn't grayed out anymore and my VM boots when I enable the option.