Remove unnecessary dependencies to synchronous 'postgres' crate (#10938)

The synchronous 'postgres' crate is just a wrapper around the async
'tokio_postgres' crate. Some places were unnecessarily using the
re-exported NoTls and Error from the synchronous 'postgres' crate, even
though they were otherwise using the 'tokio_postgres' crate. Tidy up by
using the tokio_postgres types directly.

safekeeper/Cargo.toml

@@ -31,7 +31,6 @@ futures.workspace = true
 once_cell.workspace = true
 parking_lot.workspace = true
 pageserver_api.workspace = true
-postgres.workspace = true
 postgres-protocol.workspace = true
 pprof.workspace = true
 rand.workspace = true

safekeeper/src/recovery.rs

@@ -343,8 +343,11 @@ async fn recovery_stream(
     cfg.replication_mode(tokio_postgres::config::ReplicationMode::Physical);
 
     let connect_timeout = Duration::from_millis(10000);
-    let (client, connection) = match time::timeout(connect_timeout, cfg.connect(postgres::NoTls))
-        .await
+    let (client, connection) = match time::timeout(
+        connect_timeout,
+        cfg.connect(tokio_postgres::NoTls),
+    )
+    .await
     {
         Ok(client_and_conn) => client_and_conn?,
         Err(_elapsed) => {