I think nobody here will disagree to call Tal a master of attack and Petrosian a master of defense, or Kasparov more tactical and Karpov more positional. But then, such differences would be moot for a hypothetical 32-piece tablebase. Can, what we call "playing style" (cf. "Spielertypen" by Müller & Engel, claiming there exist 4 1/2 types) be formulated in objective terms? (Offhand example: make a statistic of how close their own officers are to the enemy king in an average game.) Links to scientific papers are welcome.
I seriously doubt there are scientific papers on this. "Player styles" is probably impossible to define "objectively"/scientifically to the point where one can give a list of definite, rigid criteria that can be used by a computer to determine a player's style based on their games in a database such that everyone agrees that the computer is correct. In the end, what constitutes a distinct player style has to be arbitrarily determined at some point. In fact, I'd go so far as call an attempt to "scientifically define" player styles in this way a fool's errand.
The best kind of study one could hope for is one that tries to find clear statistically significant differences between groups of players (as chessplayers) who have different self-reported playing styles (out of a few listed), and in this sense of playing style I would be surprised if the study did not find clear differences between players who claim to be "attacking" vs. players who claim to be "solid", etc. How many broad "styles" that one should try to define is similar to how one should determine the average values of different pieces, i.e., one should do it by experience.
As a final note, one could also ask questions about objectively analyzing a specific player's unique chess style. As an example, if we feed every game that Magnus Carlsen has played up until 2021 into a neural network as training data, would the network be able to successfully pick out the games from TATA steel 2022 that were played by Carlsen? In other words, can a chess game bear the mark of Magnus Carlsen? The exciting thing about this question is that even if we are unable to describe in detail what "the mark of Magnus Carlsen" is, we can still test for whether it's there using this kind of method.
The only way to answer that question seems to be to perform a blind test. Can player A, who has played B many times before, recognize B (to whatever extent), in a series of blind games against him/her under similar playing conditions. Statisticians would have to decide just how many games that would be involve, and how many A-B pairs would need to play, as well as A-C pairs and games (where C is unknown to A, to guard against false positives, or decide just may be recognized) to produce a result with enough confidence.
If not, ... we probably are no further. But if there is a statistically significant 'recognition', we might as well call it 'style' as long as we don't have a better definition of the term.
I'm afraid that something like 1000 pairs of A-B people, 500 pairs of A-C people, and something like 50 games between each would be required, making a test impractical. But I'll leave that to the experts on statistics.