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The details of the hookup are a little confusing to me
This is how I read it.
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possible that the battery is being used to power a redox reaction in the "solution jar".
The "element wire" seems to run un-broken through the solution jar.
Since Lead is a pretty decent conductor, the voltage "across" the solution is, IMHO, smaller than any conventional electro-chemical process potential. Most reactions take a few volts. I've not bothered to look-up the copper-nickel EMF because I know it can't be over a Volt (it may be near zero?). This small battery voltage is divided between <<1 ohm in the Lead wire and >>1,000 ohms through the body.
There is "no" conventional electrochemistry happening in the solution jar.
What you do get is gold-crap or silver-crap on the lead wire.
I don't see any conventionally-rational way to believe any gold or iron or camphor flows up the wire into the body. And there are other ways to get iron or camphor if you want them. You can even buy
goldwasser, which may not heal your scar, but you could stop caring.
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break up scar tissue.
This won't put you back on the ballet stage tomorrow; nor will ultrasound or papaya injections.
Scar tissue
does get better, at least less-ugly, over the years. Therefore any long-running treatment which does no harm is liable to "do good".
My own big-scar was neatly done and quickly stitched. (Gut surgery, opened like a fish.) I know how frustrating it was to have this big stiff seam up my tummy. It is maybe 80% back to "normal" after 6 years. That first year was annoying, and 3 years before it didn't bother me every day. A car-accident must be much less neatly-ripped and not put together so quick/neat. I understand why you want this to work.
At $200+, it is cheaper than many treatments which don't do much. There is some risk your cat will drink the acid and get sick; you are wise enough to be careful. Simply laying there for 30 minutes a day visualizing the gold-flavor electrons coursing through and breaking up scar tissue may work, even if it is an illusion to focus the mind/body energy. And it gives you the idea you are "doing something" while waiting for whatever healing happens over the years.