Should this cleanup be a concern for Trisquel users too?

man machine-id says:
This ID uniquely identifies the host. It should be considered "confidential", and must not be exposed in untrusted environments, in particular on the network. If a stable unique identifier that is tied to the machine is needed for some application, the machine ID or any part of it must not be used directly. Instead the machine ID should be hashed with a cryptographic, keyed hash function, using a fixed, application-specific key. That way the ID will be properly unique, and derived in a constant way from the machine ID but there will be no way to retrieve the original machine ID from the application-specific one. The sd_id128_get_machine_app_specific(3) API provides an implementation of such an algorithm.

It would be very strange if the Tor Browser would expose the machine-id. If it needs a unique id for the OS (probably not), it hopefully uses sd_id128_get_machine_app_specific as the manual says. systemd created that API out of privacy concerns, to "discourage roll-your-own implementations or just direct use of the machine-id" (which preexisted systemd; D-BUS introduced it): https://github.com/systemd/systemd/issues/4667

In the end, rewriting the machine-id at every boot should be useless. Free software written by somebody who decides to use the machine-id without reading its man page could expose it on the network though. I very much doubt it is the case of the Tor Browser though. And messing with /etc/machine-id can create troubles such as a non-persistent journal: https://unix.stackexchange.com/questions/191313/why-is-my-systemd-journal-not-persistent-across-reboots