As I've mentioned, and this is a very personal conclusion I've come to, the Mahle Battery Extender was designed to function similar to a battery charger with current limiting at 2 amps. Why so? Because it is the safest and easiest way to use by anyone, at any time and without having to take any precautions (plug and play). As the main battery is the one that provides the greatest load demand to the engine, the extender will always go behind the main battery trying to charge it (at times when there is no load demand from the main battery.)
Do they work in parallel? Yes, at times when the motor demands current.
Now let's see what a DIY extender could look like:
1) Like the Mahle, with the main battery charger concept and current limitation always at 2amps.
2) As an additional battery in parallel and with the same current contribution to the load as the main battery. No charger approach.
Why approach 2 is not commonly used? Because it's complicated, risky, and somewhat impractical to use commercially. Not all users would be willing to learn how to use it and it could lead to lawsuits against the manufacturers that market it.
The operating principle of approach 2 is based on the use of 2 battery banks as equal as possible. That is, equal current capacity, equal voltage, equal cell technology. In our case they will be 250Wh 10S2P battery banks. Built from basic Panasonic 18650 cells. One of these banks is just the main battery, the other the extender.
If both batteries are charged to 100% and separately, in theory they will each have the same open circuit voltage. If under these conditions we connect them in parallel, the resulting voltage will be the same and since there is no potential difference between them, there will be no transient current from one battery to the other. The parallel bank will maintain the same voltage while there is no load.
When the motor demands current, that current will be supplied in equal parts by the main and the extender (either high current or low). What happens to the parallel voltage of the bank? Well, go down as current is demanded. One battery charges the other? No. Both batteries are discharged equally until reaching the protection cutoff limit of each of them.
What happens if this procedure is not strictly followed?
I will continue...