refactor(memory): remove flush_memories entirely (#15696)

The AIAgent.flush_memories pre-compression save, the gateway
_flush_memories_for_session, and everything feeding them are
obsolete now that the background memory/skill review handles
persistent memory extraction.

Problems with flush_memories:

- Pre-dates the background review loop.  It was the only memory-save
  path when introduced; the background review now fires every 10 user
  turns on CLI and gateway alike, which is far more frequent than
  compression or session reset ever triggered flush.
- Blocking and synchronous.  Pre-compression flush ran on the live agent
  before compression, blocking the user-visible response.
- Cache-breaking.  Flush built a temporary conversation prefix
  (system prompt + memory-only tool list) that diverged from the live
  conversation's cached prefix, invalidating prompt caching.  The
  gateway variant spawned a fresh AIAgent with its own clean prompt
  for each finalized session — still cache-breaking, just in a
  different process.
- Redundant.  Background review runs in the live conversation's
  session context, gets the same content, writes to the same memory
  store, and doesn't break the cache.  Everything flush_memories
  claimed to preserve is already covered.

What this removes:

- AIAgent.flush_memories() method (~248 LOC in run_agent.py)
- Pre-compression flush call in _compress_context
- flush_memories call sites in cli.py (/new + exit)
- GatewayRunner._flush_memories_for_session + _async_flush_memories
  (and the 3 call sites: session expiry watcher, /new, /resume)
- 'flush_memories' entry from DEFAULT_CONFIG auxiliary tasks,
  hermes tools UI task list, auxiliary_client docstrings
- _memory_flush_min_turns config + init
- #15631's headroom-deduction math in
  _check_compression_model_feasibility (headroom was only needed
  because flush dragged the full main-agent system prompt along;
  the compression summariser sends a single user-role prompt so
  new_threshold = aux_context is safe again)
- The dedicated test files and assertions that exercised
  flush-specific paths

What this renames (with read-time backcompat on sessions.json):

- SessionEntry.memory_flushed -> SessionEntry.expiry_finalized.
  The session-expiry watcher still uses the flag to avoid re-running
  finalize/eviction on the same expired session; the new name
  reflects what it now actually gates.  from_dict() reads
  'expiry_finalized' first, falls back to the legacy 'memory_flushed'
  key so existing sessions.json files upgrade seamlessly.

Supersedes #15631 and #15638.

Tested: 383 targeted tests pass across run_agent/, agent/, cli/,
and gateway/ session-boundary suites.  No behavior regressions —
background memory review continues to handle persistent memory
extraction on both CLI and gateway.

tests/run_agent/test_run_agent.py

@@ -3078,48 +3078,6 @@ class TestRetryExhaustion:
         assert "bad messages" in result["error"]
 
 
-# ---------------------------------------------------------------------------
-# Flush sentinel leak
-# ---------------------------------------------------------------------------
-
-
-class TestFlushSentinelNotLeaked:
-    """_flush_sentinel must be stripped before sending messages to the API."""
-
-    def test_flush_sentinel_stripped_from_api_messages(self, agent_with_memory_tool):
-        """Verify _flush_sentinel is not sent to the API provider."""
-        agent = agent_with_memory_tool
-        agent._memory_store = MagicMock()
-        agent._memory_flush_min_turns = 1
-        agent._user_turn_count = 10
-        agent._cached_system_prompt = "system"
-
-        messages = [
-            {"role": "user", "content": "hello"},
-            {"role": "assistant", "content": "hi"},
-            {"role": "user", "content": "remember this"},
-        ]
-
-        # Mock the API to return a simple response (no tool calls)
-        mock_msg = SimpleNamespace(content="OK", tool_calls=None)
-        mock_choice = SimpleNamespace(message=mock_msg)
-        mock_response = SimpleNamespace(choices=[mock_choice])
-        agent.client.chat.completions.create.return_value = mock_response
-
-        # Bypass auxiliary client so flush uses agent.client directly
-        with patch("agent.auxiliary_client.call_llm", side_effect=RuntimeError("no provider")):
-            agent.flush_memories(messages, min_turns=0)
-
-        # Check what was actually sent to the API
-        call_args = agent.client.chat.completions.create.call_args
-        assert call_args is not None, "flush_memories never called the API"
-        api_messages = call_args.kwargs.get("messages") or call_args[1].get("messages")
-        for msg in api_messages:
-            assert "_flush_sentinel" not in msg, (
-                f"_flush_sentinel leaked to API in message: {msg}"
-            )
-
-
 # ---------------------------------------------------------------------------
 # Conversation history mutation
 # ---------------------------------------------------------------------------