[Bug] Deep-research workflow loses progress on token/spend limit, restarts from zero on resume

Bug Description
Title: deep-research does not resume after hitting the token/spend limit — it restarts from zero

Summary
The deep-research skill runs as a Workflow that fans out (dozens of search +
verification subagents). When a run is interrupted by the period spend limit,
there is no durable checkpoint: the resume state lives in a session-scoped cache
(resumeFromRunId is same-session only) that is lost as soon as the session ends.
Re-invoking the skill starts a brand-new run and repeats the entire fan-out from
scratch, so the tokens already spent produce nothing.

Steps to reproduce

1. Run /deep-research on a broad topic.
2. The run hits the period spend limit and is cut off before producing any

deliverable.

1. Wait for the limit to reset, then re-run /deep-research on the same topic.
2. Observed: the run starts over from zero and consumes the whole quota again,

still with no result.

Observed behavior

• Two consecutive runs were cut off by the spend limit.
• Each run consumed 100% of the available quota and produced no final report.
• Verified, sourced claims gathered before each cutoff were only persisted in the

session transcript on disk, never surfaced as a usable deliverable.

• Re-launching the skill after the reset repeated the full fan-out instead of

continuing where it stopped.

Expected behavior

• A run interrupted by the spend/token limit should be resumable and continue from

where it stopped, without re-doing already-completed and already-verified work.

• Partial progress (verified claims) should be checkpointed to durable storage

(e.g. written out incrementally) so an interruption never results in total loss.

Impact

• Full quota burned twice with zero usable output.
• The natural recovery action (wait for reset, relaunch) actively makes it worse,

since relaunching always restarts.

Suggested fixes

• Persist run state (script + runId + completed-agent cache) durably so resume

works across sessions, not just within one.

• Add a "resume last run" path distinct from launching a fresh run.
• Checkpoint verified claims to a file/note incrementally during the run.
• Respect an explicit token/cost budget so the fan-out is sized to fit rather

than overrunning the limit.

Environment

• Claude Code, model Fable 5.
• Billing: monthly spend limit (was €40 at time of the incident).
• Skill: deep-research (built-in), running as a Workflow.

Environment Info

• Platform: linux
• Terminal: ghostty
• Version: 2.1.216
• Feedback ID: 42de5846-f4e5-4833-9989-8effed1d8a5a