Keep 5V on while sleep with LowPower library
If I read the schematics at https://spellfoundry.com/download/sleepy-pi-2-usb-c-schematic/ correctly, you need to draw continuous 5V power from the SUPPLY_5V pin instead of the SUPPLY_EXP_5V pin (the latter seems to be switched via some MOSFETs connected to pin 2 of the ATMEGA328p). Which means that you need to connect the 5V power of your second HAT to JP4 pin 3 on the Sleepy Pi HAT (instead of JP5 pin 3).