Sorry for my late reply Alfio.
However, I'm unable to provide you with a satisfactory solution here. But I can explain the reasons behind the issue and probably some suggestions:
The battery you mentioned is not listed in our compatible batteries list. Many LFP batteries on the market are generally compatible with the Pylon protocol. Regarding the issue with your battery, it would be best to reach out to the supplier you purchased the battery from for further clarification.
You mentioned that the SNA-5000 recognizes the battery of 50Ah after you tried #2. It is possible that your battery uses the older Pylon protocol, which does not transmit the battery capacity information. The BMS only adopts the Pylon protocol, where it sends a fixed capacity of 50Ah. In the newer Pylon protocol, this has been changed.
So obviously It's a BMS problem, as the inverter simply displays the information sent by the BMS and does not determine the value it delivers. For better performance, before this is solved by your battery supplier, I suggest you set a lead acid mode according to your battery's specifications.
By the way, the SNA-5000 model is currently mainly sold in Asia and Europe. May I know which country you are using it in?
Thanks