The sleeve with the broken clips at the plus terminal didn't work anymore, maybe I broke the PCB or something, it is very brittle. But I managed to remove the metal to the minus terminal and the red plastic on top of the PCB:
I measured the caps in place, so could be wrong, but it says 14 uF, for both pairs, so 7 uF each cap (seems to be parallel). The inductor is 2.2 uH, if the in place measurement is right.
The chip has some label, really hard to read it:
Looks like it says "B041" and date code 1629.
And some more train tests: I did close the lid, this should be heavier than the Batteroo sleeve, and tried it again. But I ran out of Energizer batteries, so I used a Duracell. And looks like the bunny ads are true
With the Duracell and without the sleeve, it runs for 195 minutes now, instead of 127. But there are different types of the Energizer batteries, maybe this is a type which lasts longer for lower discharge currents.
Then I used a fresh Duracell battery with the Batteroo sleeve, and the train was running for 115 minutes.
Meanwhile the first battery has recovered and I tried it without the Batteroo sleeve. It was running for 7 additional minutes! Of course, this can't be compared because of the longer recovery time and the different battery type, but I guess it will be not much different for the Energizer battery. This means the Batteroo sleeve has no positive effect at all for this train, not even the 3%, because without the sleeve most probably it would have run longer (but maybe a bit slower).
Ok, before I break the second sleeve, too, I'll send it to the next tester, @Ysjoelfir . He might be able to test it with professional EMC and ESD equipment. Was a fun project.