How do I connect Search Console and Analytics?

The connection is per project, and each project authorizes its own Google account. You open the project, click authorize, and pick the property.

That's deliberate, for two reasons. The first is scale: an agency doesn't have one Google account, it has one for each client. The second is branding: in a white label engagement, authorizing everything through one central account would put the operator's name on the client's permission screen.

A Google account can be reused across several projects, and authorizing a different account is an action right on the project screen.