Selfhosted

Having been in this same position I think I can help, you are almost definitely being cgnat which means that you do not have your own ipv4. The two workarounds I used for this are to use only ipv6 which is public but means you can't always access it from older networks. And the second solution is to wireguard tunnel to a free oracle VM and use it as a proxy.

Some German cable providers do internal NATting please check that yours does not.

If you google it, you'll find lots of similar questions for O2. I think you have to contact their customer support and get that activated once.

And have a look at your IPv4 and IPv6 addresses. Sometimes you can do it via IPv6 already, just not over IPv4 because there is some translation in the way. (In case they want too much money to give you a real IPv4 address.)

Maybe you can try if you can open your FritzBox UI from the outside with your my.fritz address. I think that has IPv6 and a port forward in place (if activated).

And btw: It's perfectly fine to do it. People need storage and online collaboration. Access to their data while away.

even allowed in Germany?

Yes.

works well on my LAN network, but when I try to make the server accessible via a DynDNS service

I guess your Fritzbox does NAT for your LAN. Then the dyndns address works only when the client is outside.

Acronyms, initialisms, abbreviations, contractions, and other phrases which expand to something larger, that I've seen in this thread:

5 acronyms in this thread; the most compressed thread commented on today has 6 acronyms.

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Do you have o2 DSL, o2 fiber, or o2 cable/coax Internet? O2 cable does not have a public IPV4 address by default, you need to request one from customer service.

Does your router indicate that you have DS-Light? I think O2 provides each customer DS-Light until they ask for a real IPv4.

To your second question: In case of DS-Light you don't need a new IPv4 IP every 24h because your IP is not public facing.

PS: I don't be sure, but the Fritz Remote Apps use IPv6 to ensure that they also work with DS-Light.

Most likely you are under CGNAT, so your best bet is Tailscale, Wireguard, CloudFlare Tunnel or Zero Tier. Pick your poison.

You checked if you have a DS-Lite contract? Those are very popular. Especially with O2, Vodafone and the fiber ISPs.
The problem: You get only an IPv4 CG-NAT IP and a regular IPv6 IP. If your ISP (for example at work) did not configure an IPv6, you will not be able to connect (A and AAAA DNS records).
I assume you set up the port forwarding in your Fritzbox (under Internet > Freigaben > Portfreigaben)?
If it has the proper external port connected to your internal port it should connect.

I had the exact same problem and the solution was to ask my ISP who then either just gave me a public IP (Vodafone) or asked for money so my network could be reached from the outside (Primerocom). So check whether there is an option with you ISP to get a "public" IP.

Can you ping your domain? How about checking the DNS resolution? What DynDns do you use?

You get a real IP? Its been cg-nat with every provider for the last many many years in Italy.

I got a cheap vps and just run some reverse tunnels to map ports from it to my home server going trough my cg-nat.

The problem was with DS-Lite tunneling, as some users mentioned, and it only works over IPv6. However, now I have another issue. My entire family has access through their ISPs, but my cellular data ISP does not support IPv6. Is there any workaround that doesn't require me to look for a new ISP or asking for IPv4 address? 😀 By the way, thanks to everyone for the help!