Tasks: Documentation for pause/resume lifecycle

Repo: coder/coder

Scope: Create comprehensive documentation for task pause/resume lifecycle feature.

Changes:

• AI agent compatibility matrix: Document which AI agents support session persistence, what context is lost without it, requirements for full support
• Persistent storage requirements guide: Document why persistent storage is needed, required paths (AgentAPI state file, AI agent session dirs like .claude/), minimum storage recommendations, troubleshooting missing storage
• Task lifecycle user guide: Document how pause/resume works (automatic pause, manual pause, resume), what gets preserved, viewing logs while paused
• Registry module README updates: Document how the AgentAPI module handles shutdown scripts, state file paths, and the new variables (state_file_path, pid_file_path, enable_state_persistence)
• Provider shutdown timeout configuration: Document how different providers may have different timeouts for allowing workspace agents to gracefully shut down, and how this will affect task snapshotting. Consider mentioning infra-based timeouts as well (e.g. Kubernetes)

Files (example):

• docs/ai/compatibility.md (new)
• docs/ai/persistent-storage.md (new)
• docs/user-guides/task-lifecycle.md (new)
• registry/coder/modules/agentapi/README.md (update)

Acceptance criteria:

• Compatibility matrix lists all AI agents with support level (full/partial/none)
• Storage guide explains persistent volume requirements with provider-specific examples
• User guide covers all pause/resume workflows with CLI and UI examples
• Registry README documents new variables and shutdown script behavior
• Integrate provider shutdown timeout configuration from #6174 and consider documenting how infra-based timeouts may also play a role (e.g. Kubernetes)
• All docs reviewed and approved before GA release

Dependencies:

• All Beta and GA issues complete

References:

• RFC: Tasks: Start/Pause/Resume Lifecycle: Documentation section
• https://github.com/coder/coder/issues/6174