These are mDNS issues, and i doubt that any .local address resolves properly.
My solution. use your routers DNS:
1- Configure your network domain name in your router, f.e. assistant.url
2- Make a DHCP reservation for your device and name it “my-esp”
3- add your domain name to ESPhome wifi settings
esphome:
name: my-esp
wifi:
ssid: !secret wifi_ssid
password: !secret wifi_iotpw
domain: .assistant.url
and behold…my-esp.assistant.url resolves in DNS…tadaaa