I am testing this currently to ensure correctness, but if you're using Android Studio via Flatpak, you may need to enable kvm permissions for the application to have hardware-accelerated VMs. This can be done using Flatseal. The relevant permission (device=kvm) is under the Device section labeled as Virtualization.
Additionally, if problems are occurring outside of Flatpak, you might need to enable certain hardware virtualization technologies from your computer's BIOS (AMD-V, VT-x, VT-d, Intel VT, Virtualization, or some other similar term depending on CPU and motherboard).
EDIT: Doing testing, it seems the default permissions provided for Android Studio's Flathub Flatpak includes device=all. No permissions edits are necessary by default. If there are problems with the /dev/kvm device not being reachable, it is almost certainly due to the necessary extensions not being enabled in the BIOS, or your CPU doesn't support virtualization. Pop! OS 22.04 has the necessary components in software for KVM to function pre-installed, so nothing should be wrong on the OS side.