Thanks everybody for the welcome.
I have already logged about 3,000 km with the bike, so I guess I can already provide some feedback.
As you are aware, the range of the bike greatly depends on factors like wind, speed, road condition, tire pressure and whatnot. Without the power tank, I was able to do about 160 km on County Roads (mostly 80 kph around here). With the power tank equipped, I can do about 200 km. That does not include excessive speeding or accelerating.
As DonTom said, it comes down to simple math. With a 25% increased battery size you get 25% increased range. The extra weight is indeed negligible.
Quite frankly, in terms of range the power tank is not as useful as I thought it would be. When you think about it, it'll initially extend your range from 160 km to 200 km and that's it. It offers no immediate benefit for shorter or longer tours. On longer tours, you need to recharge 40 km later, but it's not any faster. Or let me put it this way: if you were to go on an 800 km tour, all you would get is an initial additional 40 km, nothing else. Whether you recharge for two hours after 160 km or 2.5 hours after 200 km doesn't make any difference, it gives you the exact same range per time spent at the charger. Not really worth it.
One reason why I did it anyways is that many of my tours are 200-300 km and the extra 40 km save me half an hour of recharging time while on the road. Half an hour at the charger instead of a full hour does make a difference, whereas 8.5 instead of 9 for a longer tour really doesn't). Another, possibly more important reason is that the Power Tank probably improves battery life. We all know that Lithium batteries don't last forever and that they age from heat and high currents. Now, what is a high current? It depends. Let's ignore the actual currents and look at the C-rating. Without the power tank, the bike has a capacity of 14.4 kWh. According to the specs, the bike has 82 kw peak power, so if I ask for that power, the bike would discharge at about 5.7 C (82/14.4). That stresses the battery way more than full acceleration in my Tesla Model 3 (about 4 C, 300/75).
Same when I charge. At 6 kW (that's what I get with the SR/S Premium) it's about 0.42 C. This is not dramatic, but again, compared to what my Tesla has to endure (11.5 kW/75 kWh -> 0.15 C) it's close to three times higher.
Other differences? Yes, the Tesla has a liquid cooled battery that is always kept within reasonable parameters. The SR/S is passively cooled and has no such benefit.
Long story short: the battery has to endure way more stress than the battery in a car and that's for a good part because of its relatively small size. With a 25% bigger battery, and that's what you basically get with the Power Tank, the C-ratings go down to 4.6 C at full acceleration and 0.33 C while charging at 6 kW.
So this was my main reason to go with the Power Tank. As for the handling, I'm more driving like an old guy. I'm sure other folks would feel the extra weight right away, but to be honest with you I don't feel it at all. You'd probably have to ask someone who's going faster, I mean the power tank is in the storage compartment on top of the chargers, so it definitely increases the centre of gravity.