Do systemd-enabled WSL2 sessions ([boot] systemd=true in /etc/wsl.conf) somehow share their systemd process?

When I start two WSL2 instances (one Debian, one Ubuntu, in this case), and then do a sudo systemctl poweroff in the Ubuntu instance, the journal in the Debian WSL2 logs:

debian systemd-journald[64]: Received SIGTERM from PID 1 (systemd-shutdow).

This also happens in other contexts, like when I set a hostname with [network] hostname=ubuntu and then start it, I get:

debian unknown: WSL (2 - init-systemd(Ubuntu)) WARNING: hostname set to ubuntu in /etc/wsl.conf

I assume this is documented somehwere, but I didn't expect to be the WSL2 VMs to be this lightweight...

#windows #wsl #wsl2

I first noticed this when debugging why the WSL Interop service disappeared in my primary WSL2 instance after I shut down one of the others, and I didn't expect the cause to be that there's a cross-instance interaction via systemd that stopped all the services...
A cursory search did not turn up any information about this behaviour... Fun.