Record MultiSubnetFailover value at connection?
I don't believe this configuration setting is sent to the server.  It controls the client's interpretation of a DNS lookup returning multiple IP addresses, and there is no functional need for the server to be informed about it.  And the client doesn't send arbitrary name/value pairs to the server.  The fields that a client sends to the server are dictated by the TDS protocol, and it would require a protocol revision to add new ones.

Also while properly setting MultSubnetFailover at the client continues to be a best-practice, newer SQL Server client libraries have changed their behavior to mitigate the issues arising from not setting MultiSubnetFailover.  See Using Transparent Network IP Resolution.  Newer clients will have only a brief delay in connecting when the first IP returned from DNS is not the active AG Listener, instead of the old behavior of waiting 20-30 seconds before attempting to connect to the second IP.