Yes, it is possible to search for and export Microsoft Teams chat data for on-premises users using eDiscovery tools. However, this feature requires certain prerequisites, such as synchronizing on-premises user accounts with Azure Active Directory and assigning the user a Microsoft Teams license and a minimum of an Exchange Online Plan 1 license. Additionally, only the Teams chat data associated with an on-premises user is stored in the cloud-based storage area, and an on-premises user cannot access this storage area.
Regarding exporting Team Chats of meetings, it is not clear from your question whether you are referring to exporting chat data from a specific meeting or exporting chat data from all meetings. If you are referring to exporting chat data from a specific meeting, it is possible to download a transcript of the meeting chat by clicking on the ellipsis (...) during the meeting and selecting "Show conversation history". From there, you can select "Download" to download a transcript of the chat. If you are referring to exporting chat data from all meetings, this feature is not currently available.
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