Multitasking reduces IQ
It is less efficient. I found many years ago that I don't multitask well and need to set everything else aside to do my best whether it is writing, reading, or learning a skill. Your mind will benefit by having a full immersion in whatever you are trying to master.
I try to take this down to a micro level to get the most out of any practice and especially on a specific skill.
For instance, rather than just hitting down the line backhands no matter where the ball comes from I use a specific spin, speed, and target on a long repetition of shots to groove the stroke and refine it to perfection, or as close as I can get to it. Especially on a new skill or shot it is best to isolate and develop it to understand the individual elements needed to make it work.
The Serve Practice in Isolation
Try this on serving as well. Work on one thing such as a slice serve to the deuce court on the forehand sideline halfway between the service line and net. Take it further and work on serving from a specific spot at the baseline that will make it work for you. Most opponents won't even notice if you move a little farther to the right to get the angle on the shot. I call it indexing your serve position much like a pitcher will find the same place on the mound before starting the windup.
Spend your whole practice session on that one thing and of course stop if you notice it's bothering your arm. Not only that, but repeat this practice over the course of a week for some spaced repetition to own it. This is how you add a new skill to your list of tools on the court.