Firstly, my advice is to stop - there have been quite a few post with people having issues when updating to 2025.8.x - in addition DuckDNS seems to have been suffering more and more outages over time.
You should see if your router supports a Dynamic DNS provider and set that up. Something like https://www.noip.com/ This provides the added benefit that your router will update the server when the IP address changes - with the DuckDNS add-on there may be a delay as the add-on has to poll to see when the address changes.
Then install the Nginx Proxy Manager addon - This will allow you to use Let's Encrypt to get a certificate for the name you set-up in the Dynamic DNS provider. It also means you only need to add the IP Address for the Mginx Proxy Manager Addon to your trusted_proxes setting in configuration.yaml (ie. you are not converting your HA to use SSL by default)
If you still want help with the DuckDNS set-up you are trying to do, I can try but have a few questions:
1). Locally I can visit https://homeassistant.local:8123/ (not secure) - what do you mean by 'not secure'? do you get a certificate warning? Are you sure you are using 'https://' and not 'http://'
2). What do you have for external_url and internal_url in the mobile app? You can mask private data by saying xxxx.duckdns.org or [host].duckdns.org
3). Can you confirm DuckDNS has the correct IP? You can visit https://whatismyipaddress.com/ which should show your public ip and compare it to the one in DuckDNS.
4). What ports have you forwarded on your router (both from - to).
5). Confirm that you are forwarding from the router to the IP Address of your HA Server.
6). Tell us the changes you made in configuration.yaml for http: