Well, I understand you have to enter Home Assistant’s IP as CoIoT IP, don’t you? Wouldn’t have thought that the internal docker IP could be that wrong after it didn’t work out with the host’s IP. So what am I supposed to do then?!
I gave it another shot (from the HA server logs):
2021-12-16 22:44:14 INFO (MainThread) [homeassistant.components.shelly.utils] Starting CoAP context with UDP port 5683
2021-12-16 22:44:14 DEBUG (MainThread) [aioshelly.coap] Socket initialized on port 5683
2021-12-16 22:44:14 DEBUG (MainThread) [aioshelly.coap] Adding device 192.168.1.238 to CoAP message subscriptions
2021-12-16 22:44:14 DEBUG (MainThread) [aioshelly.block_device] aiohttp request: /settings (params=None)
2021-12-16 22:44:17 DEBUG (MainThread) [aioshelly.block_device] aiohttp response: {'device': {'type': 'SHSW-1', 'mac': 'E8XXXXXXABF7', 'hostname': 'shelly1-E8XXXXXXABF7', 'num_outputs': 1}, 'wifi_ap': {'enabled': False, 'ssid': 'shelly1-E8XXXXXXABF7', 'key': ''}, 'wifi_sta': {'enabled': True, 'ssid': 'UXXXX 1', 'ipv4_method': 'dhcp', 'ip': None, 'gw': None, 'mask': None, 'dns': None}, 'wifi_sta1': {'enabled': False, 'ssid': None, 'ipv4_method': 'dhcp', 'ip': None, 'gw': None, 'mask': None, 'dns': None}, 'ap_roaming': {'enabled': False, 'threshold': -70}, 'mqtt': {'enable': False, 'server': '192.168.33.3:1883', 'user': '', 'id': 'shelly1-E8XXXXXXABF7', 'reconnect_timeout_max': 60.0, 'reconnect_timeout_min': 2.0, 'clean_session': True, 'keep_alive': 60, 'max_qos': 0, 'retain': False, 'update_period': 30}, 'coiot': {'enabled': True, 'update_period': 15, 'peer': '192.168.1.10:5683'}, 'sntp': {'server': 'time.google.com', 'enabled': True}, 'login': {'enabled': False, 'unprotected': False, 'username': 'admin'}, 'pin_code': 'XXXXXX', 'name': 'EG Esszimmer', 'fw': '20211109-124958/v1.11.7-g682a0db', 'factory_reset_from_switch': True, 'discoverable': True, 'build_info': {'build_id': '20211109-124958/v1.11.7-g682a0db', 'build_timestamp': '2021-11-09T12:49:58Z', 'build_version': '1.0'}, 'cloud': {'enabled': False, 'connected': False}, 'timezone': 'Europe/Berlin', 'lat': 48.999962, 'lng': 8.38471, 'tzautodetect': True, 'tz_utc_offset': 3600, 'tz_dst': False, 'tz_dst_auto': True, 'time': '22:44', 'unixtime': 1639691054, 'debug_enable': False, 'allow_cross_origin': False, 'ext_switch_enable': False, 'ext_switch_reverse': False, 'ext_switch': {'0': {'relay_num': -1}}, 'actions': {'active': False, 'names': ['btn_on_url', 'btn_off_url', 'longpush_url', 'shortpush_url', 'out_on_url', 'out_off_url', 'lp_on_url', 'lp_off_url', 'ext_temp_over_url', 'ext_temp_under_url', 'ext_temp_over_url', 'ext_temp_under_url', 'ext_temp_over_url', 'ext_temp_under_url', 'ext_hum_over_url', 'ext_hum_under_url']}, 'hwinfo': {'hw_revision': 'prod-191217', 'batch_id': 1}, 'mode': 'relay', 'longpush_time': 800, 'relays': [{'name': None, 'appliance_type': 'General', 'ison': True, 'has_timer': False, 'default_state': 'last', 'btn_type': 'edge', 'btn_reverse': 0, 'auto_on': 0.0, 'auto_off': 0.0, 'power': 0.0, 'schedule': False, 'schedule_rules': []}], 'ext_sensors': {}, 'ext_temperature': {}, 'ext_humidity': {}}
2021-12-16 22:44:17 DEBUG (MainThread) [aioshelly.block_device] aiohttp request: /status (params=None)
But although it looks quite complete I get a “Failed to connect” in the HA UI after I entered that IP 
HA version (container) is core-2021.12.2, Shelly is 20211109-124958/v1.11.7-g682a0db
Any helis appreciated!
P.S.: why do I have to enter an IP in HA auf all if there is something like auto-discovery?