For me, it really depends on the game(s) I'm playing -- what the entry/stakes are and what the prizes are.
For example, when I play $11+ games...these get my full attention. Here, it is not uncommon to stay at a table for considerable time before being broken up and moved to another. As such, I need to pay more attention to individual players, id'ing those to avoid, and those to exploit. I'll often spend more time with these games playing from the computer rather than playing on the phone
App.
For public
freerolls, things are changing so quickly that it is less useful to spend that much time focussing on the opponents and be more cognizant of spots, waiting for the right opportunity to get it all in and double up.
But for really tight games, like CC Freerolls, and League games, I already have quite extensive notes on non-noobs and know the field, so it takes less concentration. In such cases, I like to do something else whilst playing poker. Often that means cooking dinner, cleaning the kitchen, doing laundry, etc.
I do get what you mean though -- in terms of playing multiple games. It can get a little more hectic when you've got 4+ games going and trying to do something else at the same time. It's kind of like how poeple tend to turn the car radio down when they're looking for a specific address.
The brain can overload with inputs making it harder to efficiently process parallel operations.
MY FAVOURITE WAY to play
online poker however, is two to four games, whilst online on Discord, with my other Poker buddies, whilst a Music bot plays tunes for us all evening. I've been playing poker with these guys for about 8 years (three online) and we golf together regularly as well as play boardgames and other card games. It was a lifeline for me during the pandemic!
Cheers,
JT