I do have a reference for you which will get you started on this topic.
The notion of "numerical target setting in performance management" is actually a part of what was once called "Scientific Management" or "Taylorism". It has its origins at the dawn of the industrial age in the first mass-production factories. What's left of this field is now a part of Industrial Engineering and falls under the broad discipline of Operations Research.
The reference I am giving is a Textbook for Industrial Engineering, which I read a few years back:
"Factory Physics, Wallace Hopp and Mark Spearman"
It's a quantitative, highly detailed and non-dogmatic approach to many of the topics that would fall under approaches like "six sigma" or the various quality control/management practices. The actual concepts in the book are implemented in ERP and MES systems which are in wide use today. The same authors have also written detailed tomes on inventory management and hospital operations.
The thing is, you're asking about "performance management" of people. The majority of the book talks about performance management of processes. There's a reason for this, and it's covered in the first section of the book which is all about the history and transformation of "Taylorism" into modern times. Basically, Taylorism only can work for very narrowly focused processes. In the early days of industrial age, managers were taught to literally treat people as resources and break down all work functions into the most basic measurable and manageable steps so that untrained workers could, in concert, fabricate complex products. The problem when this goes too far into "human resources" is that workers lose motivation and pride in their work and all this requires heavy layers of management. That hasn't prevented these kinds of approaches from being attempted in modern times. The infamous "rank-and-yank" practice is an outcome of trying to put a one-dimensional numerical values on human beings in a workplace. It works in the short term, but AFAIK, the companies that have tried this have either quit it and/or transformed it into something else.
So basically, I don't think you will find high quality research into the general performance management of "people", as that been lumped with antiquated "scientific managment and Taylorism". But there is A LOT of good material on the performance management of processes.
That doesn't prevent management consulting firms trying to implement variations of Taylorism in modern days, but if you look closely enough, it doesn't lead to good outcomes. In particular I am thinking of GE which was a once mighty company producing all kinds of innovative technology. They even pioneered six-sigma in factories and had great success with it. Along comes Jack Welch, who got it into his head that he could put numerical values on people and implement rank-and-yank and other Tayloristic practices. It was great for a while, stock price went up, "lesser performing" business units got sold off, etc. But where is GE now? It's a shell of what it once was and mostly does financial services.