/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. Some overlay filesystems do not support Birth time but that is not going to help most people unless the general populous expect all applications to be isolated in name spaces and overlay filesystems but this would have to be an expected pattern across all applications universally.

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

    stat / | grep irth | md5sum
    8b5e849954373f8f3c2a625847e4e858

But you don't have a service uploading it along with the URLs you visit, which is the creepy part. The ID itself can be useful for your own administration. And if such a service were to appear, it could easily be removed. Everything in Linux is optional, especially as long as you stick to open source.

And it’s easily altered.