Manager performance is not tied to connections data. However, manager's performance is tied to the kind of facets of team cohesion, productivity, satisfaction, and delivery that the Connections data. Does that make sense?
And it's not a terrible proxy. For example, it would be relevant if a manager was measured on their ability to hire and retain people, right? Well, if certain connections questions have a direct correlation with people leaving the team, you can imagine someone would tell the manager "Fix this connections score, or else people will leave the team."
But if they fixed the connection score, but people still left the team, they wouldn't be able to get away with that as a success. The metric is a proxy, not the target.