fix(proxy): hoist duplicate system messages before coalescing

Claude Code sends the system prompt as the top-level `system` field and,
separately, sends skill/plugin listings as `role: "system"` entries inside
`messages` (#1459 made the transformer accept those). `transform()`
unconditionally prepends the top-level field, so once both are present the
OpenAI-compat payload ends up with two `system` messages that are not
adjacent. `coalesceMessages` only merges consecutive same-role messages and
explicitly skips `system`, so it cannot fix this.

Strict OpenAI-compatible backends (LiteLLM among them) reject that shape with:
  400 A 'system' message can only appear at index 0 of the messages array.

Add `hoistSystemMessages`, run before `coalesceMessages`, which extracts every
`system` message in encounter order and reinserts a single merged one at
index 0. Content-preserving, no behavior change when at most one system
message is present.

src/proxy/transformers/request-transformer.ts

@@ -671,6 +671,49 @@ function transformMessages(messagesValue: unknown): OpenAIMessage[] {
   return translatedMessages;
 }
 
+/**
+ * Hoist every `role: "system"` message to a single leading system message.
+ *
+ * Claude Code sends the system prompt as the top-level `system` field *and*,
+ * separately, sends skill/plugin listings as `role: "system"` entries inside
+ * `messages` (see #1459). `ProxyRequestTransformer.transform` prepends the
+ * top-level `system` field unconditionally, so once both are present the
+ * resulting array holds two `system` messages that are not adjacent —
+ * `coalesceMessages` only merges *consecutive* same-role messages, so it
+ * cannot fix this case even if it did coalesce `system` (which it explicitly
+ * excludes below).
+ *
+ * Strict OpenAI-compatible backends (LiteLLM among them) reject any request
+ * where a `system` message is not alone at index 0:
+ * `400 A 'system' message can only appear at index 0 of the messages array.`
+ *
+ * This pass extracts all `system` messages in encounter order, joins their
+ * content with a blank line, and reinserts the result as the sole leading
+ * message — content-preserving, order-preserving for everything else.
+ */
+function hoistSystemMessages(messages: OpenAIMessage[]): OpenAIMessage[] {
+  const systemParts: string[] = [];
+  const rest: OpenAIMessage[] = [];
+
+  for (const message of messages) {
+    if (message.role !== 'system') {
+      rest.push(message);
+      continue;
+    }
+    const content = message.content;
+    const text = typeof content === 'string' ? content : '';
+    if (text.trim().length > 0) {
+      systemParts.push(text);
+    }
+  }
+
+  if (systemParts.length === 0) {
+    return rest;
+  }
+
+  return [{ role: 'system', content: systemParts.join('\n\n') }, ...rest];
+}
+
 /**
  * Coalesce consecutive messages of the same role.
  * OpenAI/vLLM/Ollama/Mistral require strict user<->assistant alternation.
@@ -741,7 +784,7 @@ export class ProxyRequestTransformer {
       // was billed. See:
       // https://platform.openai.com/docs/api-reference/chat-streaming
       ...(source.stream === true ? { stream_options: { include_usage: true } } : {}),
-      messages: coalesceMessages(allMessages),
+      messages: coalesceMessages(hoistSystemMessages(allMessages)),
       max_tokens: asNumber(source.max_tokens),
       temperature: asNumber(source.temperature),
       top_p: asNumber(source.top_p),