deep_research: no per-stage token budget — a single run burned ~888k tokens in Search+Verify on deepseek

[ericleepi314]

Source: PR #271:

Separately, deepseek's overall verbosity (the 888k tokens across Search+Verify) is a model characteristic, not addressed here.

Impact: /deep-research has no per-stage or per-run token ceiling. A verbose model can spend hundreds of thousands of tokens in the Search and Verify fan-out before the user sees anything, with no warning and no abort threshold. #271 fixed the Synthesize loop but the spend in earlier stages is uncapped.

Fix sketch:

• Track cumulative tokens per stage in the deep-research harness (the workflow engine already counts per-agent usage).
• Add a configurable budget (e.g. CLAWCODEX_DEEP_RESEARCH_TOKEN_BUDGET, default a few hundred k) — when exceeded, stop launching new search/verify agents, log what was skipped, and proceed to Synthesize with what was collected.
• Surface the spend in the progress UI so the user sees runaway cost early.