Possible to set default schema from connection string?

You set the default schema based on the user who is logging in via the connection, not the connection itself.

ALTER USER Mary51 WITH DEFAULT_SCHEMA = Purchasing;

Reference:

• ALTER USER

No, this is done at the database User level, not in the connection string.

For reference, here are all of the properties which can be set in a connection string: https://www.connectionstrings.com/all-sql-server-connection-string-keywords/