fix(cursor): reuse conversation checkpoints for incremental continuation

[keepitmello]

Summary

• Preserve Cursor's returned ConversationStateStructure after a successful no-tool turn and reuse that snapshot on the next validated linear continuation instead of rebuilding the full root history.
• Tool-result turns reuse the last completed-turn checkpoint plus only the uncovered suffix when the covered message boundary is known.
• Keep the existing full-replay path for compaction, helper/shadow isolation, account or model mismatch, missing/expired refs, decode failures, restart, and invalid_argument recovery.
• Bind checkpoint snapshots to conversation id, credential identity scope, and model affinity. Persist only an opaque process-local checkpointRef on Responses continuation state, and pin referenced blobs for the checkpoint lifetime.
• Do not treat OpenCodex usage or missing cache counters as a cache-hit rate. Cursor Connect still reports only usedTokens/maxTokens.

Refs #1527

Verification

What this change is supposed to prove is that a validated no-tool follow-up stops rebuilding old root history. Unit-test green is only the repo gate, not that proof.

Observed on this branch against the same Cursor account, after the local 2.24.2 process was running from this tree:

• Offline 3-turn full-replay baseline grew rootBytes 58 → 40,175 → 80,292.
• Live no-tool follow-up on this tip used continuationMode=checkpoint, same Cursor conversation id, rootBytes=0, and still answered from the prior turn (BETA-9).
• Official cursor-agent control on the same account / cursor-grok-4.6-low: turn 1 cacheReadTokens: 0 / input 18937; resume turn 2 cacheReadTokens: 18816 / new input 331 / answer ALPHA-7. OpenCodex still cannot report that counter authoritatively, so this is comparison data only.

Not shown, and not claimed:

• large-context / 429 / resource-limit reduction
• kimi-k3 or other [Bug]: Cursor adapter large-context turns collapse or rate-limit while direct Cursor remains healthy #1527 premature-completion acceptance
• tool-heavy live MCP bridge parity
• cache hit rate

Repo gate only, so a reviewer can reproduce the mechanical checks:

• bun run typecheck
• bun test tests/cursor-request-builder.test.ts tests/cursor-blob.test.ts tests/cursor-adapter.test.ts tests/cursor-discovery.test.ts tests/cursor-protobuf-events.test.ts tests/cursor-live-transport.test.ts tests/cursor-tool-continuation.test.ts tests/responses-state.test.ts
• bun run test
• bun run privacy:scan

Checklist

• Scope stays focused and avoids unrelated cleanup.
• Docs or release notes were updated when needed.
• Security-sensitive changes were reviewed for secrets, auth, and unsafe defaults.

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• All CI tests are green on my local testing.

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• I resolved all correct Codex and CodeRabbit findings.

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• review readiness checklist open (2/4 boxes ticked).

What to do

• Tick all four boxes in the PR description once you're done (currently 2/4).

Review readiness checklist

• ✅ All CI tests are green on my local testing.
• ✅ I pushed my PR to the latest dev commit.
• ⬜ I resolved all correct Codex and CodeRabbit findings.
• ⬜ My PR is ready for review.

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This PR stays in draft until every box above is ticked.