I recently got PS5 USB controller support working in the USB host shield SAMD fork (including the fancy trigger haptics), and it should also work with the USB host shield, however I don't have one to check.
Here's the PR in question:
gdsports/USB_Host_Library_SAMD#12
I thought I'd post this here in case anyone comes looking for PS5 controller support, and in hopes that someone with the usb host shield and a PS5 controller could try copying in the new files and testing if it works.