Claude Code Projects can run threads on a local machine
ClaudeDevs has added local support to Projects in Claude Code. Threads can now run on a user’s own machine.
ClaudeDevs describes a project as one conversation with Claude that splits the work into threads and passes context between them. For the desktop and web rollout, ClaudeDevs said those threads run as parallel cloud sessions and continue after the user leaves. It also said that rollout was in beta for select users.