As you drove the thread further in to MCCB focus here are some points I like to mention based on my understandings.
please let me know if the following is an example of a non-polarized DC breaker. I wouldn't buy this one, it's too cheap. I only want to understand if I have the right concept.
Amazon.it link
NO, that is not a non polarized MCCB even if there are no markings in the device, one of the picture state the below:
Also, my batteries are two BMSs which already have built-in breakers. Isn't it actually redundant that I have a breaker on the way to the inverter at all? Maybe just a disconnect switch and being done with it?
No in terms of redundancy . The breaker in the battery shall protect the cables inside the battery and towards the joint on the busbar. The theoretical intention of the MCCB after the joint is to protect the (usually) bigger cables towards the inverter. They are supposed to be bigger because your source (in the battery feeding the inverter scenario) the single battery’s supply just half of the total load.
To answer the question of a reverse connected polarity on the MCCB will solve your problem, the answer is clearly YES.
Once you engage the MCCB you will generate a spectacular “booom” , have potentially an inrush of many thousand Amp to your Inverter and you can enjoy the magic of blowing multiple electrical parts at once. Up on replacement of the inverter and deal eventual with the fire fighter you don’t need to be worry in the meantime of any connection issues on the MCCB ;-)
Joke aside. Please let me explain what a polarized Breaker means and what are the advantages.
In the event a DC breaker Trip / is disconnected it will create an arc (even at lowest current). As you deal with more than a LED such arcs become longer, be more intense and simply not extinguish themself as long energy is still “requested” from the consumer (Inverter), (or a short cut) and available from the supply (battery). To break that arc (extinguish) , is common practice to guide the arc to an so called “arc extinguishing chamber”. Such chamber will split the single arc in to tiny arcs so the overall length of the arc become longer and that lead in to a break of the arc. To speed up that process and guide the arc towards the now longer distance, permanent magnets are used.
The polarity of the magnet + the magnetic polarity of the arc will define the direction the arc is forced to go. (If correctly used it travels to the arc chamber if wrongly used the arc travel to the housing of the breaker and set it on fire at 5000 Degree Celsius. )
I Hope the illustration clarify what I mean.
If you see breaker where a + and - is on the top and on the bottom it is shown reverse IT Do NO mean a reverse connection (as assumed from you) it is the indication where the source and the load site is located.

So what looks on the first view like nonsens (while comparing the top and the bottom diagram), start to make sense when put in to account that the bottom diagram shows the in-feed (battery) in the top, where as you would need to mirror the diagram when you put the battery down and the load on top.
If you interested what DC arcs can do and how they behave please find a link below.
In my next post I will explain you the non polarized Version / what is the better and much more safe solution at all .