Hi,
Welcome to Microsoft Q&A community.
TLS Algorithm Mismatch: The error "TLS negotiation failed with error Algorithm Mismatch" indicates that there might be a mismatch in the TLS algorithms supported by the Exchange 2013 and Exchange 2019 servers. Ensure that both servers support the same TLS algorithms and that they are configured correctly.
Socket Error: The error "421 4.4.2 Connection dropped due to Socket Error" suggests that there might be network connectivity issues between the servers. Verify that there are no firewall rules or network policies blocking the communication between the Exchange 2013 and Exchange 2019 servers.
Failover Issues: The message "Attempted failover to alternate host, but that didn't succeed" indicates that the failover mechanism is not working as expected. Ensure that there are alternate hosts configured and that they are reachable.
Concurrent Connections: Exchange Server is designed to create concurrent or parallel connections to send messages to multiple destinations. If the server is configured to send all messages to a single destination, such as Exchange Online, it may limit the number of parallel and total connections, causing delays. You can change the settings to optimize performance and avoid building large queues.
Antimalware Engine: Sometimes, the antimalware engine can cause issues with email transmission. Disabling the antimalware engine temporarily and restarting the Exchange Transport Service might help resolve the issue.
To address these issues, you can:
Verify and align the TLS algorithms supported by both Exchange 2013 and Exchange 2019 servers.
Check network connectivity and ensure there are no firewall rules or network policies blocking communication.
Ensure that alternate hosts are configured and reachable for failover.
Optimize the settings for concurrent connections to improve performance.
Consider temporarily disabling the antimalware engine and restarting the Exchange Transport Service.
If you need further assistance, feel free to ask!