Switch to using the new SqlClient user-agent feature

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In #35730 (EF 10), we started injecting Application Name into the SQL Server connection string, including information about the EF version.

This was a stopgap mechanism, as SqlClient is in the process of introducing a more first-class user-agent-like mechanism for submitting such information: dotnet/SqlClient#3451, dotnet/SqlClient#3489.

Once that's done, revert #36548 and switch to the new mechanism.