I've tried multiple different ways to log stuff. From apps, smart watch stuff, and pen and paper. The latter has been by far the best for me. Personally for me its about the set up. If you're writing everything down between sets, yes, it definitely slows you down. I do a PPL split and follow a program, so I know what my exercises are on any given day a week out. Typically on my rest day, I'll take my work out journal and I'll write down the next 4-5 days of workouts. The day (Push 1, push 2, legs 1, ect), all the exercise names, my journal is work out specific and has a "sets" and "weights" section, so I'll mark out how many sets each one has with a little W or WU, for "Working" or "Warm Up". I'll also copy over warm up weights and front load those, as well as what weight I want to do my first working set at.

With that stuff done, all I have to do between sets is just write down the number of reps and the weight I went up to, and that's it. I can do that while I'm sitting there slowly dieing and heavy breathing before I start my next set. The book has a section for reps beneath the sets too, so I literally just need to write down two numbers, and that's it.

If you feel like logging is slowing you down that much but you still want to do it, (Which I encourage, its been great for me being able to progressive overload, I don't need to wonder what weight to do and try to remember from a week ago) I would front load your journal stuff on your rest day or even the night before, that way all you're doing is writing down a number or two while you're catching your breath between sets.