feat(server): filter system-injected messages from Claude conversations

Add _is_system_injected() filter to conversation.py that drops user
messages starting with known system-injected prefixes. These messages
(hook outputs, system reminders, teammate notifications) appear in
JSONL session logs as type: "user" with string content but are not
human-typed input.

Filtered prefixes:
- <system-reminder>    — Claude Code system context injection
- <local-command-caveat> — local command hook output
- <available-deferred-tools> — deferred tool discovery messages
- <teammate-message    — team agent message delivery (no closing >
                         because tag has attributes)

This brings Claude parsing to parity with the Codex parser, which
already filters system-injected content via SKIP_PREFIXES (line 222).
The filter uses str.startswith(tuple) with lstrip() to handle leading
whitespace. Applied at line 75 in the existing content-type guard chain.

Affects both chat display and input history navigation — system noise
is removed at the source so all consumers benefit.

tests/test_conversation.py:
- TestIsSystemInjected: 10 unit tests for the filter function covering
  each prefix, leading whitespace, normal messages, mid-string tags,
  empty strings, slash commands, and multiline content
- TestClaudeSystemInjectedFiltering: 5 integration tests through the
  full parser verifying exclusion, sequential ID preservation after
  filtering, and all-system-message edge case

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

tests/test_conversation.py

@@ -9,7 +9,7 @@ import unittest
 from pathlib import Path
 from unittest.mock import patch
 
-from amc_server.mixins.conversation import ConversationMixin
+from amc_server.mixins.conversation import ConversationMixin, _is_system_injected
 from amc_server.mixins.parsing import SessionParsingMixin
 
 
@@ -278,6 +278,110 @@ class TestParseClaudeConversation(unittest.TestCase):
             path.unlink()
 
 
+class TestIsSystemInjected(unittest.TestCase):
+    """Tests for _is_system_injected filter."""
+
+    def test_system_reminder(self):
+        self.assertTrue(_is_system_injected("<system-reminder>\nSome reminder text\n</system-reminder>"))
+
+    def test_local_command_caveat(self):
+        self.assertTrue(_is_system_injected("<local-command-caveat>Caveat: The messages below...</local-command-caveat>"))
+
+    def test_available_deferred_tools(self):
+        self.assertTrue(_is_system_injected("<available-deferred-tools>\nAgent\nBash\n</available-deferred-tools>"))
+
+    def test_teammate_message(self):
+        self.assertTrue(_is_system_injected('<teammate-message teammate_id="reviewer" color="yellow">Review complete</teammate-message>'))
+
+    def test_leading_whitespace_stripped(self):
+        self.assertTrue(_is_system_injected("  \n  <system-reminder>content</system-reminder>"))
+
+    def test_normal_user_message(self):
+        self.assertFalse(_is_system_injected("Hello, Claude!"))
+
+    def test_message_containing_tag_not_at_start(self):
+        self.assertFalse(_is_system_injected("Please check this <system-reminder> thing"))
+
+    def test_empty_string(self):
+        self.assertFalse(_is_system_injected(""))
+
+    def test_slash_command(self):
+        self.assertFalse(_is_system_injected("/commit"))
+
+    def test_multiline_user_message(self):
+        self.assertFalse(_is_system_injected("Fix this bug\n\nHere's the error:\nTypeError: foo is not a function"))
+
+
+class TestClaudeSystemInjectedFiltering(unittest.TestCase):
+    """Integration tests: system-injected messages filtered from Claude conversation."""
+
+    def setUp(self):
+        self.handler = DummyConversationHandler()
+
+    def _parse_with_messages(self, *user_contents):
+        """Helper: write JSONL with user messages, parse, return results."""
+        with tempfile.NamedTemporaryFile(mode="w", suffix=".jsonl", delete=False) as f:
+            for content in user_contents:
+                f.write(json.dumps({
+                    "type": "user",
+                    "timestamp": "2024-01-01T00:00:00Z",
+                    "message": {"content": content}
+                }) + "\n")
+            path = Path(f.name)
+
+        try:
+            with patch.object(self.handler, "_get_claude_conversation_file", return_value=path):
+                return self.handler._parse_claude_conversation("session123", "/project")
+        finally:
+            path.unlink()
+
+    def test_system_reminder_excluded(self):
+        messages = self._parse_with_messages(
+            "real question",
+            "<system-reminder>\nHook success\n</system-reminder>",
+        )
+        self.assertEqual(len(messages), 1)
+        self.assertEqual(messages[0]["content"], "real question")
+
+    def test_local_command_caveat_excluded(self):
+        messages = self._parse_with_messages(
+            "<local-command-caveat>Caveat: generated by local commands</local-command-caveat>",
+            "what does this function do?",
+        )
+        self.assertEqual(len(messages), 1)
+        self.assertEqual(messages[0]["content"], "what does this function do?")
+
+    def test_teammate_message_excluded(self):
+        messages = self._parse_with_messages(
+            '<teammate-message teammate_id="impl" color="green">Task done</teammate-message>',
+            "looks good, commit it",
+        )
+        self.assertEqual(len(messages), 1)
+        self.assertEqual(messages[0]["content"], "looks good, commit it")
+
+    def test_all_system_messages_excluded_preserves_ids(self):
+        """Message IDs should be sequential with no gaps from filtering."""
+        messages = self._parse_with_messages(
+            "first real message",
+            "<system-reminder>noise</system-reminder>",
+            "<available-deferred-tools>\nAgent\n</available-deferred-tools>",
+            "second real message",
+        )
+        self.assertEqual(len(messages), 2)
+        self.assertEqual(messages[0]["content"], "first real message")
+        self.assertEqual(messages[1]["content"], "second real message")
+        # IDs should be sequential (0, 1) not (0, 3)
+        self.assertTrue(messages[0]["id"].endswith("-0"))
+        self.assertTrue(messages[1]["id"].endswith("-1"))
+
+    def test_only_system_messages_returns_empty(self):
+        messages = self._parse_with_messages(
+            "<system-reminder>reminder</system-reminder>",
+            "<local-command-caveat>caveat</local-command-caveat>",
+        )
+        self.assertEqual(messages, [])
+
+
 class TestParseCodexConversation(unittest.TestCase):
     """Tests for _parse_codex_conversation edge cases."""