Same problem, where I get the message when the new cable is connected. Let it sit for 20 minutes, and powered the phone back up. Thought, if the connector on the iPhone 11 pro max had something on the pins/pads it could explain why the problem didn't show on the iPhone 12 Pro max, so I powered down the phone and cleaned the contacts with a small amount of alcohol on a slender swab. The only other piece of info that might be useful is the warning message doesn't appear right away (> 5 minutes) - so it's possible it could be a heat up issue for the monitoring circuitry.

Could be a combination of things, or different sensitivity between phones, but don't have enough info on what is being measured. Could be a iPhone 11 Pro max problem, but would think the problem would exist with the Apple manufactured cable. To confuse the matter, this problem doesn't appear when I connect this cable to an iPhone 12 pro max.

I have the same issue with some cables I just purchased when connected to an iPhone 11 pro max - this is the second batch of cables (9), so trying to determine where the problem exists.