But the fact is that stirring the tea leaves when brewing Pu-erh tea affects the tea soup.

Specifically, it affects the color and taste:
After stirring the leaves, the color of the subsequently brewed Pu-erh tea soup becomes turbid. That is to say, for tea that is not of high quality to begin with, if the leaves are stirred during brewing, the next infusion should be discarded if you want to appreciate the tea soup. Pour out the first infusion after stirring and brew another one to compensate. Due to the stirring, some other undesirable flavors will also unavoidably appear in that infusion.
This is a small technique; many people who brew tea well pay attention to this detail. From the perspective of tea brewing, a basic skill of a good tea brewer is to achieve a consistent taste across almost every infusion; one brew of tea should not have several different flavors. For some particular people, if you stir the leaves of the tea they are still brewing, it is seen as a sign of disrespect. In other words, if the tea is to be continued, the spent leaves can be shown to you, but only for looking, not for stirring.
Not stirring the leaves makes the tea more durable!
The durability of Pu-erh tea is also related to this technique. Some people who brew ancient tree tea with great care do not stir the leaves when adding water, and certainly won't allow you to stir the leaves. Brewing calmly in this way can somewhat increase the durability.
What can you see from the spent leaves?
Looking at the spent leaves, first observe the impurities in the tea soup and the residues in the tea filter. These two observations can roughly tell you about the tea's processing technique. Then look at the spent leaves and knead them. This reveals the season of the tea leaves, the integrity of the leaves, the processing technique, and any other foreign matter. In recent years, the hygiene of Pu-erh tea has greatly improved, but for some older teas, hygiene can still be an issue, with foreign matter sometimes mixed in the tea, making the use of a filter necessary.