I’m flying to the US with Lufthansa next month, and as I have no status with them, I put in my United MileagePlus FF number. I’m Premier Gold through a recent status match and thus Star Alliance Gold. I read on the Star Alliance website that, “

You can take an extra 20 kg (44 pounds) where the weight concept applies, or an extra piece where the piece concept applies.

Some airlines do not offer this benefit on individual flights, but only on connecting Star Alliance flights. Within Europe on "Light" fares offered by Lufthansa, Austrian & SWISS and "Check&Go" fares offered by Brussels Airlines, as well as on “Seat” fares offered by Air New Zealand, and "Basic" or "Light" fares by Avianca, the extra baggage allowance is not offered.”

I presume this means that I get an extra bag/more weight on my flights BLL-FRA-EWR and BOS-FRA-BLL (it’s an Economy Basic fare with one bag of 23kg included), but the Lufthansa app doesn’t reflect extra baggage allowance under my name. It just says 1 bag of max 23 kg for both me and my status-less mum and brother. Can I trust that I do in fact have extra allowance, so I don’t find myself at BLL being charged for it? Will it be more weight in one bag or an extra 20 kg bag?