[tejaskash]

What

Serializes batched flushes in AgentCoreMemorySessionManager with one lock, and fixes the retry paths that put buffered data back.

• _flush_messages_only, _flush_agent_states_only and _flush_messages run under _flush_lock.
• _flush_messages takes the agent states before the messages, so a saved state never counts a message that wasn't saved.
• A failed message flush prepends its messages, as fix(memory): restore latest agent snapshot from batched events #700 does for agent states.
• A partial agent-state failure puts back only the agents that weren't sent.

Why

With flush_interval_seconds set, the timer thread and the agent thread can flush at the same time. On main and on #700 that causes four problems:

1. A slow or failed flush of an older snapshot is written after a newer one, so read_agent restores stale state.
2. An agent state is saved while the messages it counts are still buffered. After a crash, the restored history is wrong.
3. A failed message flush puts the failed messages after newer ones.
4. When one agent's send fails, agents that were already sent are written again.

Stacked on #700. GitHub retargets this PR to main when #700 merges.

How tested

• Six new unit tests in TestConcurrentFlushes. Five fail without the fix. The threaded one passed 50 of 50 repeat runs.
• pytest tests/bedrock_agentcore/memory/: 790 passed. ruff check and ruff format --check are clean.
• End to end against a real AgentCore Memory resource in us-west-2, with injected delays and failures in front of the real create_event:
  • A real Strands agent with batch_size=3, the interval timer and Claude Haiku 4.5 restores the latest state and all 6 messages.
  • Five scenarios, one per bug, all pass. Without the fix, all five fail: stale v=1 restored twice, state v=2 with 1 stored message, stored order ['m2', 'm1'], and a duplicate agent-a event.