condenser: split summarization prompt into system + user messages

Summary

The LLMSummarizingCondenser sends its summarization request to the condenser's own LLM as a single user message that bundles both the steering instructions and the forgotten-event payload (see openhands/sdk/context/condenser/prompts/summarizing_prompt.j2).

On the OpenAI Responses API path, the event data lands in the wrong slot: a lone user message carrying the full instructions + payload is fine for Chat Completions, but it conflates "how to summarize" (steering) with "what to summarize" (data). More importantly, if the steering instructions were ever moved to system, a lone system message serializes to the instructions field with empty input (Message.to_responses_value returns a string for system; message_to_responses_dict returns [] for system), so the payload-to-summarize would never appear as a real input item.

Proposed change

Split the single summarizing_prompt.j2 template into two and send a canonical system + user message pair:

• summarizing_system.j2 -> system message (the steering instructions: "You are maintaining a context-aware state summary...")
• summarizing_events.j2 -> user message (the <EVENT> payload + "Now summarize the events using the rules above.")

This keeps the steering header in the provider's instructions/system slot and the event data in the input/user slot — the canonical shape for both Chat Completions and Responses. It also plays well with the subscription/Codex transport (transform_for_subscription), which prepends system chunks onto the first user message.

The change is isolated to the condenser's separate side-channel call (self.llm.generate(..., store=False)); it does not touch the agent's main conversation history.

Context

Discussion of how condensation works and what messages are sent to the condenser LLM. The condenser makes an independent, single-turn call to its own LLM with a freshly-built message list (no agent system prompt, no tools, no prior turns), so a system+user split is safe and semantically cleaner than the current single-user-message approach.

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

Start with openhands/sdk/context/condenser/prompts/summarizing_prompt.j2 and the LLMSummarizingCondenser call to self.llm.generate(..., store=False). Split the steering instructions and event payload into summarizing_system.j2 and summarizing_events.j2, then send them as a canonical system + user pair. Done means the steering text reaches the provider's instructions/system slot while the event payload remains in the input/user slot for both transport paths.