Battery Switch-over function is mainly dependent on voltage levels, not timing, this is the reason of why the timing information you are looking for is not specified in the documentation. Also because the ramp-down would depend on the external components. VDD is sampled. If it collapses in between samples then the event is missed and the device fails to switch to battery.
Please ensure that you keep the slew rate at 0.7V/ms or less. If the slew rate is faster than 0.7V/ms, then you can slow it down by adding some decoupling capacitors on the VDD pin.
The functionality of the battery switch-over is limited by the fact that the power supply VDD is monitored every 1 ms in order to save power consumption. Considering that the battery switch-over threshold value (Vth(sw)bat) is typically 2.5 V, the power management operating limit (VDD(min)) is 1.8 V and that VDD is monitored every 1 ms, the battery switch-over works properly in all cases where VDD falls with a rate lower than 0.7 V/ms.
I recommend you to check the Application Note AN1186 where you can find more details information about this topic, especially on section 5.3 “Battery switch-over applications”: https://www.nxp.com/docs/en/application-note/AN11186.pdf
It is not for the PCA85363A, but the battery switch-over function works in the same way.
Have a great day,
Jose
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