Could you post the specific output of the commands that don’t work? It’s almost impossible to help with just ‘It doesn’t work’. Like when ping fails, what’s the error message. Is it a timeout or a resolution failure. What does the resolvectl command I shared show on the laptop. If you enable logging on the DNS server, do you see the requests coming in when you run the commands that don’t work.
How will a reverse proxy help?
Things that a reverse proxy is often used for:
Do any of these match what you’re trying to accomplish? What do you hope to gain by adding a reverse proxy (or maybe some other software better suited to your need)?
Edit: you say you want to keep this service ‘private from the web’. What does that mean? Are you trying to have it so only clients you control can access your service? You say that you already have some services hosted publicly using port forwarding. What do you want to be different about this service? Assuming that you do need it to be secured/limited to a few known clients, you also say that these clients are too weak to run SSL. If that’s the case, then you have two conflicting requirements. You can’t simultaneously have a service that is secure (which generally means cryptographically) and also available to clients which cannot handle cryptography.
Apologies if I’ve misunderstood your situation