A THREAD FOR NEWCOMERS!

The question is, when playing through a direct connection via cable, are autosaves saved only on the server or on both computers?

I'll answer your question again.

it doesn't matter who creates

the direct connection, whether it's a poor connection, or even a single-player game.
Saves are naturally stored with the person who has them enabled.
The main thing is that the parameter EveryDaySaver = 1 is set. Whoever has it enabled will have automatic saves.

Therefore,

Autosave mode was enabled.

it's impossible for that to be the case.