Auto is rather different than P mode.
Auto also forces Auto ISO and Auto WB to be on. And flash pops up automatically. It is full Auto, like a phone camera.
But P mode does not, it is only auto exposure. But you can set these others on if you want them. If you do, you might as well use Auto.
And P mode is "scrollable", for other combinations of same exposure, but with faster/slower shutter speed.
Auto ISO might not be on, but even if it is, scrolling P mode is the SAME exposure, which is why Auto ISO is not changing. Auto ISO changes according to the light it sees in the scene (and also reacts to DIFFERENT camera exposures).
P mode scrolling is all about Equivalent Exposure.
The only real difference in P mode and A mode is that in A mode, we choose the aperture first.
P mode chooses it too, but can be scrolled to other values.
There are some small subtle differences in P mode. For example, with flash, P mode will limit the maximum aperture that can be used. This is not really about flash, it is said to be about the range of the EV meter, but the maximum aperture allowed is further stopped down 1/2 stop per each stop of higher ISO. So if planning to use your new f/1.8 lens with flash at f/1.8, then you need camera mode A or M.