RDS Proxy (Postgres) - Does `SET LOCAL` inside a transaction cause connection pinning?

From reading this article https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/rds-proxy-managing.html#rds-proxy-pinning, it seems like it does.

But from reading this Reddit comment https://old.reddit.com/r/aws/comments/10qbg64/how_much_of_an_issue_is_connection_pinning_with/j8wfo43/, it seems like it doesn't.

I know SET causes pinning, but I'd like to confirm if SET LOCAL inside a transaction causes pinning in RDS Proxy - Postgres. Conceptually, it doesn't make sense to pin as the state information is scoped to the transaction, but would like to confirm.