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.
I had actually effectively nuked my Linux log files permanently on my first Ubuntu install back in 2011. I did that by mapping all the log files to ramfs on startup, and clearing all the logs still on storage to zero bytes.
I didn’t do that out of any paranoia or anything, I did that because I had Linux fully installed on a mere 4GB USB flash drive, so I wanted to eliminate as many unnecessary write cycles as I could possibly manage.
I also set the temp folder and internet cache to ramfs, much improved performance over the typical setup on a USB2 flash drive.