Synapse is unable to cleanly `shutdown` homeserver after failing to `setup`

[MadLittleMods]

Synapse is unable to cleanly shutdown homeserver after failing to setup. Like when it fails to connect to the database for whatever reason.

Discovered while writing some Complement tests for Synapse Pro for small hosts: https://github.com/element-hq/synapse-small-hosts/pull/204

Sister issue to #19189

Reproduction

# XXX: Use some homeserver config that has an invalid database path for SQLite3
homeserver_config = HomeServerConfig.load_config(
    "Synapse Homeserver", argv_options
)
hs = create_homeserver(homeserver_config)
hs_ref = weakref.ref(hs)

try:
    # We expect this to explode at this point because it's unable to connect to the database
    setup(hs)
except Exception as exc:
    # Cleanup on failure
    await hs.shutdown()

# Cleanup the internal reference in our test case
del hs

# Force garbage collection.
gc.collect()

hs_after_shutdown = hs_ref()
if hs_after_shutdown is not None:
    self.fail("HomeServer reference should not be valid at this point ")