Tasks: Beta documentation for pause/resume lifecycle

[mafredri]

Repo: coder/coder
Parent: #1271 (GA documentation)
Umbrella: #1248

Context

#1271 covers GA documentation for task pause/resume. This ticket scopes the Beta subset: enough for users and template authors to understand and use the feature.

Scope

• Task lifecycle: How tasks pause (automatically via workspace TTL, manually) and resume. What gets preserved, what doesn't. Log snapshot visibility while paused.
• Persistent storage: Required for the feature to work. Without it, AI agent session files and AgentAPI state are lost on stop.
• Graceful shutdown: Shutdown scripts must complete for log snapshots and state persistence to work. What happens when they fail (best-effort).
• Module configuration: How template authors enable/disable pause/resume support via registry modules. enable_state_persistence is exposed on all AI agent modules (enabled by default).
• Agent compatibility: Which agents support pause/resume and at what level (full/partial/none). Claude Code is the only verified full-support agent.

Not in Beta scope

Remains in GA #1271:

• Full agent compatibility matrix (blocked on #1329)
• Registry module README updates (depends on #1257)
• CLI docs for coder tasks pause/resume/send
• Detailed provider shutdown timeout guidance (#6174)

Dependencies

• #1257, #1258 (module configuration)

References

• RFC: Tasks: Start/Pause/Resume Lifecycle