For the record:
If you have a Unifi network and you activate the HomeKit functionality on Home Assistant, remember to add the MAC address of the host where HA is installed to the list of the wired hosts that are allow to broadcast on the Wi-Fi network. This is found under your Unifi network setup: settings --> Wireless Networks --> (edit your Wi-Fi network) --> Advanced Options --> Multicast and Broadcast Filtering.
If you do not do so and “Block LAN to WLAN Multicast and Broadcast Data” is active, your HA will not show up on the HomeKit app after entering the pin_code
.
NB: For better performance on the Wi-Fi network, I would recommend you to keep the “Block LAN to WLAN Multicast and Broadcast Data” option active.