Microsoft has published an article explaining how to search for Teams chat history in the web UI when in an Exchange Server Hybrid environment. This article indicates PowerShell can be used to perform the search but that it is also possible to search from the web admin center if you open a case with Microsoft to have this provisioned into your tenant.

The article can be found here: https://docs.microsoft.com/en-us/microsoft-365/compliance/search-cloud-based-mailboxes-for-on-premises-users?view=o365-worldwide

I opened a case to add this to a client tenant and Microsoft support is not yet able to do this. Please enable Microsoft support teams to deploy this feature as advertised to our client's tenants.