synapse crashes after switching to postgresql

Error during initialisation:
     Traceback (most recent call last):
       File "/home/user/synapse/env/lib/python3.11/site-packages/synapse/app/homeserver.py", line 359, in setup
         hs.setup()
       File "/home/user/synapse/env/lib/python3.11/site-packages/synapse/server.py", line 348, in setup
         self.datastores = Databases(self.DATASTORE_CLASS, self)
                           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       File "/home/user/synapse/env/lib/python3.11/site-packages/synapse/storage/databases/__init__.py", line 72, in __init__
         with make_conn(database_config, engine, "startup") as db_conn:
              ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       File "/home/user/synapse/env/lib/python3.11/site-packages/synapse/storage/database.py", line 165, in make_conn
         native_db_conn = engine.module.connect(**db_params)
                          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       File "/home/user/synapse/env/lib/python3.11/site-packages/psycopg2/__init__.py", line 122, in connect
         conn = _connect(dsn, connection_factory=connection_factory, **kwasync)
                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
     psycopg2.OperationalError: connection to server on socket "/var/run/postgresql/.s.PGSQL.5432" failed: FATAL:  Peer authentication failed for user "synapse_user"


 There may be more information in the logs.
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synapse.app.homeserver(homeserver.yaml) failed to start (exit code: 1). Check the Synapse logfile, or run synctl with --no-daemonize.