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.

tests/unit/proxy/transformers/request-transformer-regressions.test.ts

@@ -321,4 +321,32 @@ describe('ProxyRequestTransformer regressions', () => {
 
     expect(result.tool_choice).toBe('auto');
   });
+
+  it('merges the top-level system field with a mid-array system message into one leading system message', () => {
+    // Claude Code sends the main system prompt via the top-level `system`
+    // field AND a skill/plugin listing as a `role: "system"` message inside
+    // `messages` (see #1459). Prepending the top-level field unconditionally
+    // used to leave two non-adjacent `system` messages in the payload, which
+    // strict OpenAI-compatible backends (LiteLLM among them) reject with:
+    // `400 A 'system' message can only appear at index 0 of the messages array.`
+    const result = new ProxyRequestTransformer().transform({
+      system: [{ type: 'text', text: 'You are Claude Code, a CLI tool.' }],
+      messages: [
+        {
+          role: 'system',
+          content: 'The following skills are available for use with the Skill tool:\n- foo',
+        },
+        { role: 'user', content: 'ping' },
+      ],
+    });
+
+    const systemMessages = result.messages.filter((message) => message.role === 'system');
+    expect(systemMessages).toHaveLength(1);
+    expect(result.messages[0]).toEqual({
+      role: 'system',
+      content:
+        'You are Claude Code, a CLI tool.\n\nThe following skills are available for use with the Skill tool:\n- foo',
+    });
+    expect(result.messages[1]).toEqual({ role: 'user', content: 'ping' });
+  });
 });

tests/unit/proxy/transformers/request-transformer.test.ts

@@ -43,7 +43,7 @@ describe('ProxyRequestTransformer', () => {
     });
   });
 
-  it('accepts Claude Code system messages in the messages array', () => {
+  it('accepts Claude Code system messages in the messages array and hoists them to a single leading system message', () => {
     const transformer = new ProxyRequestTransformer();
     const result = transformer.transform({
       messages: [
@@ -53,10 +53,14 @@ describe('ProxyRequestTransformer', () => {
       ],
     });
 
+    // Strict OpenAI-compatible backends (e.g. LiteLLM) reject any payload
+    // where `system` is not alone at index 0, so a mid-array `system`
+    // message must be hoisted rather than left in place. See #1459 for why
+    // the message must be accepted at all, and the coalesce-duplicate-system
+    // fix for why it can't simply stay where it landed.
     expect(result.messages).toEqual([
-      { role: 'user', content: 'hello' },
       { role: 'system', content: 'answer tersely' },
-      { role: 'user', content: 'which model is this?' },
+      { role: 'user', content: 'hello\nwhich model is this?' },
     ]);
   });