Clean up AnalyzeConversationAsyncLROPoller logic before GA/next beta

During PR review (https://github.com/Azure/azure-sdk-for-python/pull/42271), concerns were raised about the current patched poller implementation. Specifically:

**1. Last state handling**

- Right now _patch.py contains logic to capture the last operation state (poller._last_state) via a deserializer hook. Instead, we should move this logic into the custom poller itself by overloading base methods like wait() or result(). This keeps the patching minimal.

**2. Exposed details**

- poller.details currently includes errors and next_link. These should not be surfaced: if there's an error it should already get raised. And next_link is already handled by the ItemPaged that is returned in result.