[SSE Completion - Issue 3] Multi-round + interleaving streaming test coverage

[ashwing]

Part of #118.

No integration test drives a multi-round gateway streaming loop and asserts the client-visible frame sequence — the loop tests in dispatch_loop_cassette_test.rs are non-streaming, and the one streaming case is single-round. The defects in the sibling sub-issues all ship unnoticed because of this.

Add cassette-backed streaming tests asserting the exact client frame stream across ≥2 gateway rounds:

• exactly one response.created / lifecycle envelope
• monotonic sequence_number (incl. synthetic + terminal frames)
• contiguous output_index
• no <think> in output_text
• interleaved thinking + tool_use in one turn

These lock the behavior the other sub-issues fix and guard against regression.

[harivilasp]

Coordination note: PR #132 covers the #119 GatewayAccumulator behavior fix and includes a regression for the multi-round public stream invariants: single lifecycle, monotonic sequence_number, and contiguous output_index.\n\nI am intentionally keeping #121 open because it describes broader streaming coverage, including interleaving and no-think-output assertions beyond this focused fix.