Proxy: improve http-pool (#6577)

## Problem

The password check logic for the sql-over-http is a bit non-intuitive. 

## Summary of changes

1. Perform scram auth using the same logic as for websocket cleartext
password.
2. Split establish connection logic and connection pool.
3. Parallelize param parsing logic with authentication + wake compute.
4. Limit the total number of clients

test_runner/regress/test_proxy.py

@@ -393,11 +393,11 @@ def test_sql_over_http_batch(static_proxy: NeonProxy):
 def test_sql_over_http_pool(static_proxy: NeonProxy):
     static_proxy.safe_psql("create user http_auth with password 'http' superuser")
 
-    def get_pid(status: int, pw: str) -> Any:
+    def get_pid(status: int, pw: str, user="http_auth") -> Any:
         return static_proxy.http_query(
             GET_CONNECTION_PID_QUERY,
             [],
-            user="http_auth",
+            user=user,
             password=pw,
             expected_code=status,
         )
@@ -418,20 +418,14 @@ def test_sql_over_http_pool(static_proxy: NeonProxy):
 
     static_proxy.safe_psql("alter user http_auth with password 'http2'")
 
-    # after password change, should open a new connection to verify it
-    pid2 = get_pid(200, "http2")["rows"][0]["pid"]
-    assert pid1 != pid2
+    # after password change, shouldn't open a new connection because it checks password in proxy.
+    rows = get_pid(200, "http2")["rows"]
+    assert rows == [{"pid": pid1}]
 
     time.sleep(0.02)
 
-    # query should be on an existing connection
-    pid = get_pid(200, "http2")["rows"][0]["pid"]
-    assert pid in [pid1, pid2]
-
-    time.sleep(0.02)
-
-    # old password should not work
-    res = get_pid(400, "http")
+    # incorrect user shouldn't reveal that the user doesn't exists
+    res = get_pid(400, "http", user="http_auth2")
     assert "password authentication failed for user" in res["message"]