Thank you for your help.
In our design, the VDD_P2, VDD_P4, VDD_ANA, and VDD_BAT pins are connected to VDD. VDD_P3 is left floating (port P3 is not used).
VDD_CORE rises well after VDD (see attached oscillogram: channel 2 = MCU_RESET_B pin, channel 1 = VDD, channel 3 = VDD_CORE).
On the reset pin, we have a capacitance of 100nf and a resistance of 10K (the 100 Ohm resistor R193 and switch SW1 are not present).