Help needed: homeassistant.local:8123 refuses to connect, while on :4357 it does

After installation of Home Assistant OS on raspberry pi5 it functioned, then after some integration tries no connection in local LAN with homeassistant:8123 (same with IP.local:8123) is possible.
homeassistant:4357 still works

Hi Andrej, welcome to the forum!

If you have not configured your HA to be accessible over HTTPS/from WAN, make sure your browser uses http:// and doesn’t switch automatically to httpS://
Alternatively, use the IP address: http://X.X.X.X:8123 (replace X.X.X.X with your Raspberry Pi’s IP address)