fix(example): avoid duplicate streamed response deltas

[abetlen]

Fix streamed Responses API events from duplicating the first output delta.

• Snapshot mutable output item and content part payloads before later stream-state mutations.
• Covers reasoning text, normal output text, and tool call item-added events.
• Validated with synthetic Responses stream chunks and python3 -m py_compile examples/server/server.py.