It’s been a while, but I believe this video was where I heard it. From memory (I’m out right now and can’t rewatch to verify) it was specifically the per-kilometre carbon emissions, not taking into account manufacturing costs.
Obviously there’s some fuziness depending on your diet and the power source used for charging. A vegan who would be charging in a coal-powered grid is going to look better, relatively speaking, for an analogue bike than someone who eats multiple kilos of red meat every week who has solar panels.
I’m not vegan, but I largely replaced by cycling calories w/ oats when I biked to work for a few years, and my area is largely powered by coal and natural gas (not sure on the exact ratio). I haven’t done the math, but I’m guessing I would come out ahead of an electric bike, especially if we included manufacturing and shipping costs for the motor and battery.