Like you mentioned, that in your experience it leave you groggy, personally I think this depends on the person and how their body reacts to beer. I've found that one beer (500 ml) at least an hour or two before sleep doesn't leave me groggy in the morning at all. If I drank beer right before sleep that probably wouldn't work well.

I'm not sure that this is 100% accurate!

While it does have more of a sedative effect than alcohol, I don't think you can count is as healthier unless you're eating it or vaporising it!

Also in my (entirely subjective) experience I find it harder to wake up in the morning, given the same amount of sleep as sober days. No 'hangover' as such, but definitely feel more groggy for the first hour or so after waking!