I remember running Linux Router Project [0] on a 1.44mb floppy disk back in the late 90s! Of course, it didn't have a GUI, but I don't think you could even fit the linux kernel on a single floppy disk today.
Technically, you can compile the 6.8 kernel using "make tinyconfig" (which results in a 509kb image). Of course, this isn't usable on actual hardware, but it is a good baseline to build off.
In 2000, I was using Yellow Dog Linux on a Power Mac 7500 for this.
I even had it set up to use "dial knocking" to force it to connect remotely and send me an email with its IP address so I didn't need dynamic DNS.
In addition to NAT for my Ethernet (10BASE2) connected devices, it provided an Internet connection to my Telnet-accessible PDP-11/73 (15.2 MHz CPU, 4MB RAM, 456 MB hard drive [14" / 36 cm platters, 148 lb / 67 kg]) running 2.11BSD via SLIP.
0: https://en.wikipedia.org/wiki/Linux_Router_Project