[SSE Completion - Tracking] Coherent multi-round gateway streaming

[ashwing]

Overview

Gateway-owned tool streaming works today — gateway calls are hidden from the client and synthetic web_search_call/mcp_tool_call frames stream in real time. But the client-visible SSE stream isn't reconciled into one coherent response across gateway rounds, and a separate reasoning-carry-forward bug leaks <think> markup into the visible answer.

Validated live against a current-main gateway (0385d6f) → vLLM (Qwen3) on a 2-round web_search stream (1411 client frames). The evidence below is observed, not inferred.

What's already correct (not in scope)

• Gateway-owned function_calls are hidden from the client stream (0 leaked in the live run).
• Synthetic tool-call frames stream in real time.
• Per-round terminal frames are suppressed; a single terminal is emitted at the end.

Work breakdown

• [SSE Completion - Issue 1] Unify the client-visible stream across gateway rounds (GatewayAccumulator) #119 — unify the client-visible stream across rounds (GatewayAccumulator)
• [SSE Completion - Issue 2] Prior-turn reasoning leaks <think> into the visible answer #120 — stop feeding prior-turn reasoning back into the loop (<think> leak)
• [SSE Completion - Issue 3] Multi-round + interleaving streaming test coverage #121 — multi-round + interleaving streaming test matrix

Live evidence summary

Symptom	Observed (2-round stream)
response.created emitted per round	2 (should be 1)
sequence_number across rounds	resets 953 → 0 at round 2; terminal chunk is null
output_index across rounds	resets 3 → 0 (round-2 output collides with round-1)
<think> in visible output_text	present — root-caused to reasoning carry-forward
multi-round streaming test coverage	none