[checkpoint] Resume cline_agent sessions

Parent

Child of #3221 and #3024.

Runtime state

responses_api_agents/cline_agent/app.py delegates authoritative continuation state to the Cline process, session database/data directory, and project tree.

Provider adapter requirements

Implement the shared opaque-runtime contract with provider/version, native session or thread ID, safe-boundary sequence, isolated workspace/session bundle manifest and digest, model-call lineage, resource/MCP metadata, exact resume operation, and stale-process fencing. Advertise export/restore only after native resume is proven; otherwise declare restart-only explicitly.

Acceptance criteria

• Retain per-run session/DB directories through commit and resume the captured session rather than deleting or sharing them.
• Kill and replace the agent server after each provider-emitted completed turn, then resume without duplicated model/tool effects.
• Session databases and workspaces are isolated by rollout attempt.
• Old processes cannot emit responses or mutate state after replacement.
• Missing, corrupt, or incompatible bundles fail restore before activation.
• Duplicate resume is idempotent or rejected deterministically.

Start with responses_api_agents/cline_agent/app.py, then read the parent issues #3221 and #3024 for the shared opaque-runtime contract. Trace how continuation state is delegated to the Cline process, session database/data directory, and project tree. Done means isolated bundles can be safely committed and resumed, replacement processes are fenced, and invalid or duplicate restores fail deterministically.