Yes, TinyCore-Core comes without a GUI (like the commenter above said, headless). When they say 28 MB RAM, that might even be overestimating it a bit. All of TinyCore-Core fits into just 17 MB. Of course that goes up if you need to install things, and I don’t know if it comes with an ssh-Server out-of-the-box. So for a proper server setup, 28 MB sounds pretty reasonable.

http://tinycorelinux.net/

It blows my mind, that there is an entire Linux Distro, that fits into a modern processor’s cache. Who needs RAM anyways? (unfortunately, because of how cache works, we can’t actually use it without RAM)

If you run your services off of a homelab rack that dims the lights whenever you power it on

If you are in this situation, then you definetly should get some more power, or at least a UPS to make sure you don’t trip a breaker.