fix(matrix): skip events received before bot startup

Matrix sync replays the room timeline on each startup or `/restart`,
causing already-handled messages to be reprocessed (#3553). Even with
`store_sync_tokens=True`, the sync token isn't reliably re-injected
when restoring a session via access_token + load_store(), so the
client re-reads recent timeline entries.

Filter `event.server_timestamp` against the process start time so old
events are dropped at the `_on_message` / `_on_media_message` entry
points. Trade-off: messages received during downtime won't be
processed, which matches the issue reporter's expectation.

Closes #3553

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

tests/channels/test_matrix_channel.py

@@ -380,6 +380,62 @@ async def test_on_message_skips_typing_for_self_message() -> None:
     assert client.typing_calls == []
 
 
+@pytest.mark.asyncio
+async def test_on_message_skips_pre_startup_event() -> None:
+    channel = MatrixChannel(_make_config(), MessageBus())
+    client = _FakeAsyncClient("", "", "", None)
+    channel.client = client
+    channel._started_at_ms = 1_000_000
+
+    handled: list[str] = []
+
+    async def _fake_handle_message(**kwargs) -> None:
+        handled.append(kwargs["sender_id"])
+
+    channel._handle_message = _fake_handle_message  # type: ignore[method-assign]
+
+    room = SimpleNamespace(room_id="!room:matrix.org", display_name="Test room")
+    old_event = SimpleNamespace(
+        sender="@alice:matrix.org", body="old", source={}, server_timestamp=999_999
+    )
+    fresh_event = SimpleNamespace(
+        sender="@alice:matrix.org", body="fresh", source={}, server_timestamp=1_000_001
+    )
+
+    await channel._on_message(room, old_event)
+    await channel._on_message(room, fresh_event)
+
+    assert handled == ["@alice:matrix.org"]
+    assert client.typing_calls == [
+        ("!room:matrix.org", True, TYPING_NOTICE_TIMEOUT_MS),
+    ]
+
+
+@pytest.mark.asyncio
+async def test_on_media_message_skips_pre_startup_event() -> None:
+    channel = MatrixChannel(_make_config(), MessageBus())
+    client = _FakeAsyncClient("", "", "", None)
+    channel.client = client
+    channel._started_at_ms = 1_000_000
+
+    handled: list[str] = []
+
+    async def _fake_handle_message(**kwargs) -> None:
+        handled.append(kwargs["sender_id"])
+
+    channel._handle_message = _fake_handle_message  # type: ignore[method-assign]
+
+    room = SimpleNamespace(room_id="!room:matrix.org", display_name="Test room")
+    old_event = SimpleNamespace(
+        sender="@alice:matrix.org", body="old", source={}, server_timestamp=999_999
+    )
+
+    await channel._on_media_message(room, old_event)
+
+    assert handled == []
+    assert client.typing_calls == []
+
+
 @pytest.mark.asyncio
 async def test_on_message_skips_typing_for_denied_sender() -> None:
     channel = MatrixChannel(_make_config(allow_from=["@bob:matrix.org"]), MessageBus())