fix(session): stop training the model to parrot [Message Time: ...]

Past assistant turns in history were prefixed with "[Message Time: ...]"
just like user turns. The model treated these as in-context demos and
started prefixing its own replies with the same marker, leaking
metadata to the user. Prompt-level warnings could not beat dozens of
prior assistant samples.

Annotate only user turns and proactive deliveries
(_channel_delivery=True, i.e. cron / heartbeat pushes whose timing is
the whole point and which are too infrequent to act as demos). Adjacent
user-side timestamps still pin every normal assistant reply for
relative-time reasoning. The now-redundant identity.md warning is
removed along with the demonstration source.

tests/agent/test_context_prompt_cache.py

@@ -188,14 +188,15 @@ def test_identity_has_no_behavioral_instructions(tmp_path) -> None:
     assert "Execution Rules" not in identity
 
 
-def test_system_prompt_treats_message_time_as_metadata(tmp_path) -> None:
+def test_system_prompt_does_not_warn_about_message_time_markers(tmp_path) -> None:
+    """Parroting is prevented by not annotating assistant turns in history;
+    no prompt-level warning about ``[Message Time: ...]`` is needed."""
     workspace = _make_workspace(tmp_path)
     builder = ContextBuilder(workspace)
 
     prompt = builder.build_system_prompt()
 
-    assert "Historical messages may include `[Message Time: ...]` prefixes" in prompt
-    assert "never quote, copy, or include those markers" in prompt
+    assert "Message Time" not in prompt
 
 
 def test_default_soul_template_contains_execution_rules() -> None: