Your local IP address is 127.0.0.1, among other addresses.
On a private network, your external or public IP address these services return is the IP address of your firewall. Not of your local Mac or NAS or whatever other server box you’re using behind the firewall.
If you’re trying to expose your server or NAS to the whole of the internet, and your server will get probed, it will get targeted, and potential latent issues and vulnerabilities will get checked, then you will need configure port forwarding through your firewall into your server, and map he incoming connection into your server. Basically, exposing a server gets multiple free vulnerability checks, but you won’t get the report.
Put differently, you will need to provide a direct path in through your firewall for untrusted and potentially malicious users (which means either dynamic DNS or a static IP and static DNS, and port forwarding TCP port 80 and TCP port 443 on the firewall), and if the miscreants do manage to breach the server—which can happen from time to time—they’re then operating directly on your server, and with the rest of its contents. And quite possibly then with the rest of your local network. (I usually prefer using a so-called DMZ configuration, to isolate a potential breach. Fixing exploited one server is a whole lot less work than potentially fixing everything else on a local network that might not have been maintained entirely up to date and entirely securely.)
Your external address would be your IP address followed by whatever local path in the server. You can set up dynamic DNS (DDNS) to map to that, or can get a fixed (static) IP address from your ISP and can then use traditional DNS. DDNS works best when the firewall supports that, too.
Say that web service returned 198.51.100.11 as your public IP address. With port forwarding enabled on the firewall, he path to your server would be http://198.51.100.11/rest/of/path and https://198.51.100.11/rest/of/path — the rest of the path is determined by your web server, and your picture folder would have to be configured within whatever web server you’re using here.
The OzoneLord-2026 stuff is a local mDNS / Bonjour / ZeroConf network name, and is not available publicly; outside your firewall.
Some ISPs also block some network traffic on residential (dynamic) service tier, as well.
I’d suggest using iCloud Photos picture hosting, or using some other not-local service. I would not recommend exposing a Mac or a NAS to the internet. Not unless you want to learn a whole lot about networking, IP routing, port forwarding, web servers, and security, that is. Because you will learn about all that, and more.