Here's something fun.
Apparently the Apple II emulator AppleWin can get online using the Contiki OS. Here's the emulator:
And here's disk images of Contiki OS compiled for Apple II:
And here's the instructions for getting online:
My understanding of those instructions is that I need to get another IP address from my ISP. I don't really want to pay for that. But... the idea looks pretty cool.
I did try Contiki OS in the emulator. Pretty cool!