I don't know how windows scaling works for games, but the principle as you described, if we take 1920x1080 and we have 400dpi, if we put 720 and stretch it, 400dpi x2 get 800. If we don't stretch 720 in the game and play in the black bars, the 400 dpi will stay the same on the monitor, that is, there will be no increase.
As for the multiplier in the game and dpi, the shooting is on a 2D monitor and the movement is on a sphere. There is a fixed distance of 360 and people write about it as "sens" in the game.
Let's say we have 20 cm, and these 20 we will feel on a 2D monitor at different FoV 120 and 60 in WZ, at 60 sharp and at 120 inert.
You can also measure the path in monitors and pixels:
360\120=3*1920=5760 total path in pixels
360\60=6*1920=11520 total path in pixels
S=c(monitors); t=l;
When the angle of view changes, the speed of the pointer changes, the path does not change, the path is a circle 360=20cm. When the viewing angle is 60, to cover the distance, you need to spend from edge to edge 6 monitors, but you need to match the path of 20cm on the mouse pad. At 120 it is already 3 monitors, and since the monitors are physically the same - one characteristic in length, in order to traverse a circle of 360 degrees around its axis, the cursor must move slower. Therefore, when setting FoV 120, there is a fisheye effect and the cursor becomes inert. If you set it to 60, the cursor will be very sharp, despite the fact that the character will move as if slowly, it will be difficult to aim. 120 the character will be fast, but the cursor will be inert (slow). This is all related to the multiplier "a", it starts to appear and affects the fact that the equality is fulfilled. Multiplier "a" depends on viewing angle, speed (speed depends on viewing angle, but in general they are complex)
c,l are length units (cm, m, inches, pixels, etc.)
C(the length of the circle in the game)=a(the product of some multiplier)*l(the length traveled by the mouse on the mouse pad). The a1 multiplier depends on the viewing angle(60), on the pointer movement speed, on the sensitivity in the game, not on dpi, sens. - is the speed of the pointer movement.
The "c, l" of the path depends on dpi. The speed of movement depends on "sens.
let's hypothetically imagine that the path of the mouse from edge to edge on the mouse pad equals one monitor. For the equality 6=a60*1(figuratively, these numbers(6;1;) are not values, they include a complex of numbers) and 3=a120*1 for this equality to hold, a60≠a120. That is, the multipliers "a" are not equal, that with different viewing angle, different dependence of "v" speed, different dependence of "sens." sensitivity, we can call them synonymous v=sensitivity, sensitivity=v.