I noticed that you mentioned you are still On-Prem Exchange.
Do you have an Exchange hybrid deployment?
If not, it may not be possible for Teams to integrate with Exchange on-premises.
Here is a link about the prerequisites and troubleshooting: Troubleshoot Microsoft Teams and Exchange Server interaction issues
Please refer to Issue 1: A delegate cannot schedule a Teams meeting on behalf of a delegator, which may be the same issue in this case.
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