Add test for proper handling of connection failure to avoid 'cannot wait on socket event without a socket' error (#8231)

## Problem

See https://github.com/neondatabase/cloud/issues/14289
and PR #8210 

## Summary of changes

Add test for problems fixed in #8210

## Checklist before requesting a review

- [ ] I have performed a self-review of my code.
- [ ] If it is a core feature, I have added thorough tests.
- [ ] Do we need to implement analytics? if so did you add the relevant
metrics to the dashboard?
- [ ] If this PR requires public announcement, mark it with
/release-notes label and add several sentences in this section.

## Checklist before merging

- [ ] Do not forget to reformat commit message to not include the above
checklist

---------

Co-authored-by: Konstantin Knizhnik <knizhnik@neon.tech>

test_runner/regress/test_pageserver_reconnect.py

@@ -2,6 +2,7 @@ import threading
 import time
 from contextlib import closing
 
+import psycopg2.errors
 from fixtures.log_helper import log
 from fixtures.neon_fixtures import NeonEnv, PgBin
 
@@ -40,3 +41,26 @@ def test_pageserver_reconnect(neon_simple_env: NeonEnv, pg_bin: PgBin):
                 c.execute("select pg_reload_conf()")
 
     thread.join()
+
+
+# Test handling errors during page server reconnect
+def test_pageserver_reconnect_failure(neon_simple_env: NeonEnv):
+    env = neon_simple_env
+    env.neon_cli.create_branch("test_pageserver_reconnect")
+    endpoint = env.endpoints.create_start("test_pageserver_reconnect")
+
+    con = endpoint.connect()
+    cur = con.cursor()
+
+    cur.execute("set statement_timeout='2s'")
+    cur.execute("SELECT setting FROM pg_settings WHERE name='neon.pageserver_connstring'")
+    connstring = cur.fetchall()[0][0]
+    cur.execute(
+        f"alter system set neon.pageserver_connstring='{connstring}?some_invalid_param=xyz'"
+    )
+    cur.execute("select pg_reload_conf()")
+    try:
+        cur.execute("select count(*) from pg_class")
+    except psycopg2.errors.QueryCanceled:
+        log.info("Connection to PS failed")
+    assert not endpoint.log_contains("ERROR:  cannot wait on socket event without a socket.*")