What is the purpose of tehillim at shemira?
Based on the gemara, the Shulḥan Aruch states (YD 344:16):
אין אומרים בפני המת אלא דברים של מת כגון צרכי קבורתו והספד אבל שאר כל דבר אסור והני מילי בדברי תורה אבל במילי דעלמא לית לן בה
Before a dead body, we only speak of matters of the dead, like their burial needs or eulogy, but all other matters are forbidden; and this concerns words of Torah, but for all other matters, we don't mind.
The Rambam says essentially the same thing (Hilchot Avel 13:9). Ramban (cited in Beit Yosef on Tur YD 344) says that "matters of the dead" are the laws of eulogy, taking out the body, and burial. Namely: Torah study encompassing practical currently needed information.
On the other hand, it is common (and apparently recommended) for the people watching over the dead body before burial (sitting shemira) to say tehillim (psalms). See, for example, here and here and here and here.
In order for this to be permitted, according to the halacha as stated above, I assume that the tehillim are "matters of the dead", but I don't understand in what way. Can someone please explain how saying tehillim is a "matter of the dead"? I would prefer a non-mystical explanation, if possible; I suppose that one exists, since R. Yosef Qaro, a very mystically-inclined person, still wrote what he wrote above in the Shulḥan Aruch.