Now I'm much more of a generalist, and because I work in ML instead of niche physics, there is a whole lot more to go through. So mostly I don't: I get a few newsletters that let me select new papers I'm interested in, and my work takes me down rabbit holes that result in deep-ish rabbit holes where I do the usual find some key papers based on google search and then go through the references (and citations) to get more papers in that area.
Otherwise, I find that the gap is very small between when something new comes out and when it's rolled into some of the common frameworks e.g Pytorch lightning- although that's discipline specific obviously. Come to think of it, I also look at papers with code, the benchmarks section, to see what the state of the art for different datasets is. And if I have time I look through accepted papers at the key conferences.
Anyway, if i had to summarize (my experience only): researcher -> go to as many conferences and talk to as many people as you can; practitioner -> don't worry about missing this week's buzz, and dig in as required.
A caveat is that one can spend so much time keeping up-to-date that one's own research languishes.