Upper time bound for simple (non-research) greedy searches (~2 min)

[apmantza]

Summary

Simple greedy_search calls (individual engines and engine: "all" without depth: "research") have no overall wall-clock deadline. Only per-extractor runExtractor timeouts exist (src/search/engines.mjs:21-40): 60s default, 70s gemini, 80s chatgpt, 120s logically.

Problem

Total time for one tool call can exceed 2 minutes because multiple budgets stack:

• engine: "all" fans out to N engines (each up to 60-80s) + source fetching after all engines finish (bin/search.mjs)
• Visible-recovery retry re-runs a blocked engine in visible mode after the headless attempt already timed out
• A single extractor's in-browser eval can hang until the CDP/nav timeout (e.g. logically burned the full ~113s on answer-wait today)

Requested behavior

In depth: "research" mode the per-round budgets already exist (src/search/research.mjs). For simple (non-research) searches, add a hard overall ceiling — ~2 minutes — that caps the entire call (fan-out + source fetch + any visible recovery), kills in-flight extractor children, and returns a clear TimeLimitExceeded error so the caller isn't left hanging.

Constraints:

• Must still return partial results if some engines finished before the deadline (consistent with the resilient-synthesis design).
• Apply to the CLI path (bin/search.mjs) and the Pi tool path (src/tools/greedy-search-handler.ts).
• Research mode must remain unaffected.