The official rules do not mention a way to play with the Automa but without the Shadow Empire. As BGA strives to adhere to official variants only, I assume they have similarly adhered to the official way of playing a solo game of Tapestry. This means you can only play a solo game with both the Automa and the Shadow Empire.
From the Automa rulebook:
"This rulebook introduces a system for adding two artificial players, the Automa and the Shadow
Empire. They take the place of human players and are collectively known as bots.
You can use the Automa and the Shadow Empire together to play by yourself or you can use just
the Shadow Empire with 2 human players. For the latter, read the separate rule sheet.
To reduce your effort, the Automa and Shadow Empire play by their own simpler rules. Any rule
not explicitly overridden here is still in effect, which includes you following the multiplayer rules."
