Containers within VMs are a norm for security in cloud-native [1]. Some lessons there could be applied to desktop.
One option is the approach of Spectrum OS [2]. They use crosvm (same as what Firecracker "micro VMs" uses) and virtio_wl [3][4].
Another approach might be x11docker [5] with Kata Containers [6].
Curiously, the work for WSLg (WSL with graphics) [7][8] to support graphical Linux guest VMs could also be applied on a Linux host.
1: https://archive.fosdem.org/2020/schedule/event/kernel_address_space_isolation/attachments/slides/3889/export/events/attachments/kernel_address_space_isolation/slides/3889/Address_Space_Isolation_in_the_Linux_Kernel.pdf
2: https://spectrum-os.org/
3: https://spectrum-os.org/design.html
4: https://alyssa.is/using-virtio-wl/
5: https://github.com/mviereck/x11docker
6: https://katacontainers.io
7: https://github.com/microsoft/wslg
8: https://xdc2020.x.org/event/9/contributions/611/attachments/702/1298/XDC2020_-_X11_and_Wayland_applications_in_WSL.pdf