I did check for older models as well. Even dug up some stove catalogues from the 70s and 80s to be extra sure. I just genuinely cannot confirm your numbers. I'm about as confident in my unit confusion hypothesis as I can reasonably be.
I'm sure you had the experiences you're recounting, but as far as the numbers go, they do not seem to explain them. Especially since these are the burner ratings, before the heat transfer losses.
If I do accept the unit confusion on your behalf:
15K BTU (your biggest gas burner) -> 55% efficiency (optimistic) -> 8250 BTU reaching the pan
3.6 kW (cheap plug-in induction stove) -> 80% efficiency (pessimistic) -> 10045 BTU reaching the pan
It just doesn't compute.
the main burner is two-row high somewhat like
https://www.hallsintl.com/heavy-duty-gas-stove-2-burners-15k...
If you do get the chance to figure out the exact model you have at home, please do let me know here. Won't blame you if you don't though, I appreciate this is a chore.