Good call, I double checked and you seem to be right.
I found the github issue tracking this: https://github.com/flatpak/flatpak/issues/4311
This is easy to state but a lot less easy to solve.
Hiding /etc/machine-id isn't going to be a meaningful improvement if "other device identifiers" can't be hidden. The most obvious one is the MAC address of each network interface, which is globally unique and available to all processes that have network access.
To prevent access to the machine ID, xdg-dbus-proxy would have to block all org.freedesktop.DBus.Peer.GetMachineId() calls, which is an incompatible change. That method was intended as a way to determine whether two processes on the bus are running on the same machine; with hindsight, it would have been better as IsOnSameMachine(s: unique_name) -> b on the message bus, rather than GetMachineId() -> s on each peer, but running untrusted software was not really a thing when the Peer interface was designed 15+ years ago.
Just goes to show how much deeper these problems are than they appear on the surface. Design decisions from 15+ years ago haunting software of today
P.S. You can shorten your command to simply flatpak run --command=bash org.torproject.torbrowser-launcher -c "cat /etc/machine-id"
I use --command=bash a lot when I want to just enter a shell inside the flatpak environment