I find a plug-in watt meter the best way to see what's happening with many appliances, such as battery chargers. I've used one a lot for ten years. Sometimes I wanted to monitor two things at once, so I bought another one the other day. It's another brand because Amazon had a price spike in Kill-a-Watt.
I'll second your vote for the Kill-A-Watt; I've used them for well over a decade (most recently for some before/after data when doing major upgrade surgery on my workstation), but too lazy to ever put one on my Rad charger; thanks for the details.
For sort of a semi-permanent Kill-A-Watt with second-by-second historical data collection, logging and website/phone access, this works pretty darn well for a reasonable price:
https://amzn.to/3JN8IvGNote that since your power usage data passes through their servers, they make their money by selling that data to others, presumably "anonymously" but who knows. That has some interesting features, though, such as being able to hook up to many power companies to get their rate data automatically - useful if you're billed differently depending on day of week or time of day. I got the 4-pack to monitor a fridge, freezer, my workstation and a space heater.