[gpt-oss] Parse output msgs refactor

[daniel-salib]

Purpose

Refactor parse_output_message function in
vllm/entrypoints/harmony_utils.py to improve code
maintainability and readability. The function was
becoming too complex with multiple nested conditional
branches for handling browser tools, function calls,
MCP calls, and message parsing.

This PR extracts the logic into focused
sub-functions:

• _parse_browser_tool_call() - Handles browser tool
  calls with JSON parsing
• _parse_function_call() - Handles function calls
• _parse_mcp_call() - Handles MCP calls
• _parse_reasoning_content() - Handles
  reasoning/analysis content
• _parse_final_message() - Handles final message
  output

No functional changes - purely a code organization
improvement.

Test Plan

Run existing tests to ensure no behavioral chang

[qandrew]

thanks for putting this together! One thing to keep in mind for the future is that MCP tool calls are constructed from two harmony messages as it's both an reasoning item and tool out right now, when we implement that we can build off of this PR