No external URL advertised using MDNS

Configuration
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Hello,

I use Home Assistant, core installation.
For external access, Nabu Casa is my friend :slight_smile:

When I open a terminal and use avahi-browse to read how Home Assistant announces itself using MDNS, I see external URL is empty.

$ avahi-browse -rtl _home-assistant._tcp
+ enp3s0 IPv4 Maison                                        _home-assistant._tcp local
= enp3s0 IPv4 Maison                                        _home-assistant._tcp local
   hostname = [xxx.local]
   address = [IP4_addr]
   port = [8123]
   txt = ["requires_api_password=True" "base_url=http://<ipv4>:8123" "internal_url=http://<ipv4>:8123" "external_url=" "version=2023.9.2" "uuid=xxx" "location_name=Maison"]

As I specified, I use Home Assistant Cloud for external access so the external URL should be my Nabu Casa URL.

When I checked some months ago, external URL was set.
Unfortunately I don’t find anything which could help to know when this issue begun.

What could cause this issue?