Based on the following scenario, what stage of team performance would you consider this team to be currently in? You are part of an organizational team. For the three years prior to a new member joining the team, performance was high. In the year after the new member joined, performance has gone down. The new team member has a slower than usual growth curve. A few months after being employed, the existence of a minor medical issue made it possible for the new team member to avoid some responsibilities. Since that time, the team’s workload has also increased. It would seem as though the team is overworked at this point, and it is starting to take its toll on the team’s overall performance and motivation.

I believe the question is asking about Bruce Tuckman's four stages of team development. He wrote about the four stages in his 1965 article titled "Developmental Sequence in Small Groups." What's great about Tuckman's four stages is that they are easy to remember because they rhyme. The four stages of team development are "forming," "storming," "norming," and "performing."  
Based on the question, it seems that the team has been in the performing stage for the past three years. Everyone knew their roles, the leader was clearly identified, there was a common goal everybody worked toward, and there was very little (if any) friction among group members.  
Unfortunately, the addition of the new group member who doesn't learn quickly and can't do as much as the rest of the team members has knocked the team performance out of the performing stage. I wish I could say the team only moved back one stage to the norming stage. The norming stage is characterized by team members beginning to "gel" together and figure out where individual strengths are best applied. Team members in this stage usually get along with each other, but group performance isn't at peak levels yet. This is where the team in the question should be with the addition of a new member. One new member shouldn't be able to throw off all the group cohesion established over the previous three years; however, I think the new group member has pushed the team all the way back to the storming stage. 
The following is a brief summary of the storming stage:

Storming often starts where there is a conflict between team members' natural working styles. People may work in different ways for all sorts of reasons but, if differing working styles cause unforeseen problems, they may become frustrated. 

The above paragraph fits well with the scenario described in the question. There is conflict between team members about workloads, and it is causing frustration among existing group members.  It would be especially frustrating in your example because the previous, slightly smaller team can recognize the team no longer performs at peak levels.  
https://hr.mit.edu/learning-topics/teams/articles/stages-development

https://www.mindtools.com/pages/article/newLDR_86.htm