Linux distros log a TON about what you’re doing by default.
Tonnes of software uses systemd-journald to log errors, the bash shell saves everything you type into the terminal, and wtmp, btmp, utmp all track exactly who is logged in and when, and the kernel uses dmesg to log a bunch of stuff.
While the system isn’t sending these logs to Microsoft or Google, anyone who gets into your system like police or hackers can see almost everything that you have been doing.
If you want to be private, you must disable them.
This feels like bait. But really the answer is encrypt your disks or use something fully ephemeral if you are that paranoid about your hardware physically being compromised. Disabling all of your system logs which do not leave your system and removing any visibility you have is quite honestly the best way to screw yourself over. How are supposed to know if a system is compromised if you are covering your eyes and ears for the sake of obscurity?