Cf. https://www.postgresql.org/docs/current/protocol-replication.html

Basically, we need to instruct the backend to go into logical
replication walsender mode in order to be able to use commands like
`CREATE_REPLICATION_SLOT` which are necessary to be able to seamlessly
transition from an initial snapshot into the WAL streaming.

Copy-both mode is initiated when a backend in walsender mode executes a
START_REPLICATION statement.

Also remove an unecessary mut

Don't use sqlx_postgres as its API isn't stable.
Use sqlx itself as a dev-dependency instead.

Use something similar to PgListener