Run everything inside your Ubuntu 22.04 proot. I didn't test this yet using chroot.
Addons_Proot_PlayOnLinux_Box.sh will do this for you. Make sure you run it through Addons_Menu.sh.
Lack of binfmt can affect how the PlayOnLinux will run the x86 or x64 Wine version, but luckly Bash Box86_64 and undocumented BEFORE_WINE prefix can help to mitigate these problems.
Installation is quite simple and basic.
apt install -y playonlinux
The only difference is that you will have to mention what the Box86_64 version you want to use in order to run Wine, through the BEFORE_WINE flag. E.g.:
BEFORE_WINE=box86 playonlinux
BEFORE_WINE=box64 box64 playonlinux
Note that the PlayOnLinux would not run as root, so you need to run it as another user.