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Auto FP is not affected by aperture or camera mode. Any mode, any aperture. It is affected by shutter speed.
Exposure is affected by aperture, but not flash mode.
Auto FP only changes the flash. Instead of being the regular instantaneous speedlight flash pulse, it becomes a continuous light, on just before the shutter opens, until just after the shutter closes. Continuous in relation to the shutter, but like a desk lamp is always on. Continuous light works at any shutter speed, like the Sun outdoors, there is no concept of sync. This is kinda of a big deal, but then, so is regular speedlight flash too.
When actually in the continuous mode (which I call HSS, High Speed Sync, using the faster shutter speed), then the FP flash exposure has
equivalent exposures just like sunlight does:
1/400 f8 is equivalent exposure as 1/800 f/5.6 or 1/1600 f/4. True of FP flash and sun too, all continuous light.
Regular speedlight flash is faster than the shutter speed, and does not work that way... is same flash exposure at any usable shutter speed.
Flash exposure does still fall off fast with distance, like regular speedlight flash mode also does.
The FP shows up anytime the Auto FP option is selected. It only actually does HSS flash (the continuous light mode) only when the shutter speed is actually set faster than the maximum sync speed (actually, only when faster than the E1 menu selection - your camera has two choices).
So... the flash action changes drastically when changing from 1/320 second to just faster at 1/400 second.
I think of the FP showing up as a warning, that big changes are "armed" and can occur simply by changing shutter speed.

If in camera A mode outdoors, such a change can happen without our being aware.
HSS flash mode suffers from having only about 20% flash power available (in order to be continuous).
This high shutter speed HSS flash seems pointless (to me) for macro flash. Regarding stopping motion, the speedlight flash mode is already faster than any shutter speed, and we need f/16 for macro.
HSS is typically for portraits in the park, if we seek to use f/2.8 in daylight (allowed with flash by HSS and maybe 1/3200 second shutter). It is low power, but bigger speedlights are usually just sufficient for fill flash at reasonably close range, maybe ten feet.
There is quite a bit to it, and try first reading
Four Flash Photography Basics we must know - Auto FP and HSS
Then if still any questions, ask away.