I understand that in a research lab or in academia, this is common practice. But in the more menial coding industry that most of us are probably in, how do you find time for this? Do people read papers in their spare time and discuss over lunch, or are there enlightened managers who support this during working hours?

Good question. Most people read the paper on their own time, and we meet over lunch. The meetings themselves are just an hour, so it's not a massive time block. I've found that the people who show up are the ones who are genuinely curious and would be reading this stuff anyway (and sometimes just need a commitment/accountability to do it). Having a group gives them a reason to do it on a schedule.