/etc/machine-id also exists

Indeed. One can regenerate it on each shutdown / reboot. The process is a little different depending on whether one has systemd or not. It's a dbus thing but systemd ingests it and there is a specific process around updating that in systemd.

There is also the NetworkID in Firefox about:networking#networkid

Another trackable piece of information on most systems is the creation time of / which just about any application can query unless it is properly isolated. This can be turned into a short unique hash. There are hacky ways to change the Birth time on unmounted filesystems using debugfs which may result in corruption.

    stat / | grep irth
    Birth: 2023-04-17 20:27:01.000000000 +0000

    stat / | grep irth | md5sum
    8b5e849954373f8f3c2a625847e4e858