How to do Downtime in AMNESIA
The concept of an always running game can be difficult to grasp for people used to only doing periodic sessions.
It's handled in an in character groupchat with my players. (Ceres and Alice are NPCS, and thus, me).
It's a facsimile of our characters literally having a groupchat. Between sessions, people send messages as their characters.
In world, this conversation took place over about 10 minutes, but the actual conversation stretched over several days, since players were interacting whenever they were free.
Personally, this is one of my favorite parts of AMNESIA.
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Here's a downtime that took place between sessions. As you can see, this single downtime event was added to whenever people were free to do so. (Daedalus is the narrator, or me. There was a bit of a metanarrative in the old OATH campaign)
As you can see, I sent the narration a day after maria @totally-zoe sent her contribution, but it didn't interrupt the flow of the story, because downtime is designed to be played at the leisure of the players and GM, between sessions.
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During downtime, the players have a lot more roleplay agency. There often arent any checks or rolls during downtime, so players are free to dictate the results of their actions. It's a way to keep the game going with casual roleplay between sessions.