[Document] Add document about client initialization behavior for mgmt

The context is here: https://github.com/Azure/azure-sdk-pr/issues/2454#issuecomment-3680426377

Thanks to @weidongxu-microsoft for finding this issue.

The bot's [anwser](https://teams.microsoft.com/l/message/19:7c0ef487fa6e4e2ab8a925fd3a18efe3@thread.tacv2/1767511463925?tenantId=72f988bf-86f1-41af-91ab-2d7cd011db47&groupId=39910aef-85da-4e30-b5e3-35f04ef38648&parentMessageId=1767511458763&teamName=Azure%20SDK%20Q%26A%20Bot%20Testing&channelName=Azure%20SDK%20QA%20bot%20for%20Java%20Testing&createdTime=1767511463925) contains incorrect context on the client initialization for mgmt. So we need to add a doc.