How does a government, even though unelected, go about impounding or destroying all privately owned modern technology? What enforcement powers have they got?

It was never there in the first place. The first inhabitants of these communities (which don't include the whole planet; I imagine there are a double handful of them on most continents - the neuros and the genderless kids are more or less universal, though) were volunteers who, prior to joining under the auspices of a rich eccentric individual, were very poor and didn't have their own personal electronics. There was nothing to take, and joining was an improvement because it came with access to the communal resources.

Of course there could be any number of uninteresting answers, like 'they've got a singleton' or 'they're ruled by an AI that moved all of humanity into a simulation world it built from scratch'.

Nope. No AI.

What do these contended pain-free people actually do with their time?

What they like. They go places, look at things, read stuff, listen to music, hang out with their friends. Most of them have jobs. I find it a little puzzling that you have trouble thinking of how one could fill one's time without significant economic competition.