Opinions vary on whether the BCR can damage things, but I will point out one fact. A BCR (supercap) looks like a direct short when you first turn it on, and so it does put a much larger load on the charging circuit until the cap gets at least a partial charge on it. As to whether that is detrimental to the charging circuit remains open to conjecture.
I personally think a good design of a battery replacement would add an inrush limiter to allow the capacitor to charge more slowly without putting an excessive load on the charging circuit.
I've seen a couple 5V boards that apparently bit the dust right after installing a BCR. However, 5V boards have a reputation for biting the dust if you look at them funny, so it's hard to say if the BCR figured into the failure. I've seen plenty of 5V boards bite the dust with no BCR in sight, so there's that...
I recently had an issue of a shorted board on a Premier ps2 /3 volt. The engine was purchased on the Bay with a Popular supplier's BCR2 installed. It ran for some time until recently. On start up now the only life it shows is a faint buzzing noise from the tender. 😣
The negative shrink tubing and black wire insulation coming out of the BCR2 had melted to the OUTSIDE of the male connector from the speaker wires. I didn't see any bare wire from the BCR2 negative side but it must have been pretty hot. Also a red charging circuit wire connected to the BCR2 had melted itself to a larger gauge orange wire with no continuity established between the two.
I found there to be continuity between the pins on the removed BCR2 and another one that I had from the popular supplier. I also found the same result with one that I had from you. So I figured things should have been OK .
JUST A COUPLE QUESTIONS John :
1.) The BCR2s from the popular supplier are rated at 5.4 v and your caps is rated at 5v. Any significants reason?
2.) Is there a different connection that I should make with your caps with the MALE connector end instead of the FEMALE end found on the other BCR2s ?
AND FINALLY.......the only place I could find an issue with the tender itself was that one wire had broken loose at the speaker . I couldn't say if it may have contacted the metal speaker housing or not. 🤔
Thanks John.