54.4V is 0.2V too low. Not huge, and if the battery were a year or two old, I wouldn't worry about it. However, this battery is brand new.
0.2V could be just an inaccurate meter. If spread across multiple parallel groups, not such a big deal. HOWEVER, if this 0.2V is ALL in one, single parallel group, in a brand-new battery, could indicate a defective cell or bad weld, or similar. A cell which will not charge fully is often also a cell which will sag in voltage dramatically under load.
"impossible to switch on using button on display", BUT, R & R the battery, NO CONNECTION TO CHARGER, and the switch works. BMS has NOT been reset by a charge, but the controller has been reset by removing power. Controller LVC has been activated.
Incorrect LVC settings are common, however the voltage displayed before cutoff is in the correct range.
CRITICAL INFORMATION NEEDED - "when I'm on a climb" - THIS IS THE EVENT THAT CREATES THE SHUTDOWN!!!! TWICE!! How LONG, in distance, How much TIME, in minutes, and How much CLIMB, in feet of altitude, is involved ????????? Rough estimates are OK. There are MOUNTAINS, in France. Also need an estimate of your level of pedaling effort during the climb.
Also need to know EXACTLY how much weight is being carried on the bike.
BOTH shutoff events occurred during a climb. This is a high load event. HOW HIGH that load is, is a critically important piece of data.
The voltage drop is pretty steep, though this depends on the climb data. You could have a seriously defective battery which may represent a clear and present danger to yourself and those around you. Take care to store the bike far away from any flammable materials, outside the home.
The testing needed will involve opening the battery, and accessing the sense wire connector on the BMS itself. Tedious, you will need a DVM with a readout containing at least two decimal places, just one is not good enough. I would investigate warranty coverage first, also test the output of the fully charged battery, and multiple times during a long ride. The display voltage could be off significantly, and 47V, that is 3.6V per cell, is at the point where voltage sag starts to really accelerate. The amount of stored power is not linear, this is well over half-depleted.
EDIT: Need the Amp-hour rating of your battery.