goal judge: split judge prompt into system + user messages

Problem

judge_goal() in openhands-sdk/openhands/sdk/conversation/goal/judge.py builds its LLM request as a single user message with no system message before it:

response = judge_llm.completion(
    messages=[Message(role="user", content=[TextContent(text=prompt)])]
)

Placed at lines ~65–66. The prompt embeds JUDGE_PROMPT (steering/format instructions) together with the objective + transcript.

This violates the repo convention that every LLM request starts with a system message (see parent tracking issue #5144). It also means the judge's verdict format instructions live in the user slot rather than the system/instructions slot, which matters for the Responses API path where a lone user message ends up entirely in input.

Proposed change

Split the judge request into a canonical system + user pair:

• system message carrying JUDGE_PROMPT (the steering / verdict-format instructions).
• user message carrying the objective + transcript payload.

Alternatively, prepend a small system message with the shared judge role definition. Either way the request must begin with a system role.

Parent issue: #5144

Note: the judge is an independent, single-turn, side-channel call (judge_llm.completion(messages=[...]), forced stream=False); it builds its message list from scratch and does not touch the agent's main conversation history, so adding a system lead-in is safe and isolated.

This issue was created by an AI agent (OpenHands) on behalf of juanmichelini.

Open openhands-sdk/openhands/sdk/conversation/goal/judge.py and inspect judge_goal() around lines 65–66, along with the request conventions tracked by issue #5144. Verify how JUDGE_PROMPT and the objective/transcript are assembled, then run the relevant judge or SDK tests. Done means the independent request starts with a system message and preserves the existing verdict behavior.