By default the SoC doesn't actually enter low power mode when shutdown on the Pi 4/5; I believe this has to do with some HAT and peripheral issues that don't really affect most users (specifically, if the 5V rail is still on while the 3.3V rail is off, which is what low power mode amounts to).
It can be changed via the EEPROM configuration; you can see the current values this way:
> rpi-eeprom-config [all] BOOT_UART=1 POWER_OFF_ON_HALT=0 BOOT_ORDER=0xf41
You want to change POWER_OFF_ON_HALT to 1, which you can do with sudo -E rpi-eeprom-config --edit.
For more about that: https://www.raspberrypi.com/documentation/computers/raspberry-pi.html#raspberry-pi-bootloader-configuration