Stack UPS HAT with Picade X HAT

I have a Picade with Pi 4 4Gb setup, with retroArch manually installed on top of raspberry pi os.
On top of that, it’s running Home Assistant in docker with a USB zigbee/zwave controler from GoControl.

I’d like to keep it running as uninterruptible as possible, so I am thinking of adding a UPS HAT.

I am thinking of pijucice, it’s only using 2 i2c pins and the power supply pins.
I plan to put the pijuice HAT on the Pi4, then stack the Picade X HAT on top. But I’m not quite sure how to manage the power supply from the Picade HAT yet.

Do you have any recommendations? Thanks!