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>

amc_server/mixins/conversation.py

@@ -3,6 +3,21 @@ import os
 
 from amc_server.config import EVENTS_DIR
 
+# Prefixes for system-injected content that appears as user messages
+# but was not typed by the human (hook outputs, system reminders, etc.)
+_SYSTEM_INJECTED_PREFIXES = (
+    "<system-reminder>",
+    "<local-command-caveat>",
+    "<available-deferred-tools>",
+    "<teammate-message",
+)
+
+
+def _is_system_injected(content):
+    """Return True if user message content is system-injected, not human-typed."""
+    stripped = content.lstrip()
+    return stripped.startswith(_SYSTEM_INJECTED_PREFIXES)
+
 
 class ConversationMixin:
     def _serve_events(self, session_id):
@@ -57,7 +72,7 @@ class ConversationMixin:
                         if msg_type == "user":
                             content = entry.get("message", {}).get("content", "")
                             # Only include actual human messages (strings), not tool results (arrays)
-                            if content and isinstance(content, str):
+                            if content and isinstance(content, str) and not _is_system_injected(content):
                                 messages.append({
                                     "id": f"claude-{session_id[:8]}-{msg_id}",
                                     "role": "user",