DW has done small-batch canned jam on our 10 year old GE Profile induction stove. She did say it was somewhat annoying to get the water up to temp. I'm not sure if that was because of power limits, or because she was probably using the huge 5 gal stock pot we use to brine turkey for thanksgiving and an extra deep rack for the jars (think 1+ inch) so likely needed to heat way more water than would have been necessary had she had an appropriately size pot.
She also successfully makes turkey broth using the same pot, post-thanksgiving. She usually has a couple of gallons in there when she does it, plus veggies, bird carcass, etc. Brings it up to boil, runs it on a boil for a while and drops it down to simmer for a couple hours.
Our induction stove has a fan to keep its electronics from overheating that it'll run. I have seen it drop power down, although it is *usually* related to too much power demand not overheating. We can't run all the burners on high, that'd blow the circuit if we could force them all to high, so the stove is auto-limiting itself to not do that. That's actually true for pairs of burners on the configuration our stove is (paired burners have a max wattage, so you can't run both of the pair on high, although you can run them both on 7-8ish, so that's usually good enough anyway).
It is a GE Profile. I don't know the exact model number and its somewhat irrelevant, because it is old enough I'm sure you can't buy it anymore. Think 10+ years. The controls and burner layout is similar to their current one fwiw:
https://www.geappliances.com/appliance/GE-Profile-30-Smart-Free-Standing-Convection-Range-with-Induction-PHB920SJSSThey are... not cheap. Ours is still going though, a decade later. We have picked up some minor scratching on the surface. We are pretty careful -- we have nice stainless steel (inductable) pots and make sure the pots and the stove are both clean. I stir fry (in a paella pan), so I do end up moving the pot while its on the stove. Its held up remarkably well, honestly.