So is this normal for agencies or is the same thing done at other product companies as well?
First, I found that it dropped productivity massively. One of the documented conditions for flow is "A loss of reflective self-consciousness". When time tracked, even in 30-60 hour, non-screenshot blocks, I'd be unable to get into flow. I'd also feel secure in justifying that I was getting work done, so while the monitor was showing work, the work was not in my head.
Second, screenshots doesn't stop me from procrastinating. I have two PCs at all times and a phone. 3 min build times meant that I had plenty of excuses.
Third, nobody cares, and clients think it's kinda dumb. They don't care if you're working 1 hour or 10. Most people rather pay fixed cost over time based. When untracked, I'd effectively log about half as many hours for the same amount of work. So time tracking ended up arguing that I should be paid half my hourly rates.
I mostly tracked to get more accurate estimates and log productivity (e.g. how much sleep or diet actually affects things). But the act of logging has been so detrimental to productivity that I just avoid it now.
Management complains but not much they can do besides deduct money or fire me. And when pay doesn't keep up with inflation then I really couldn't care less.
Sometimes those reasons apply, sometimes they don't.
The reasons range from contractually driven such as an external time and materials contract with a customer who will perform an audit at one end of the spectrum to internal org charts where staff are fungible such as the Amazon warehouse.
In both cases the ultimate source is company culture...or rather in all cases (where a company does or doesn't track like that).
Good luck.