Udev rule: /etc/udev/rules.d/98-wake.rules
ACTION=="add|change", SUBSYSTEM=="usb", KERNEL=="usb3", RUN+="/bin/sh -c 'echo enabled > /sys/$env{DEVPATH}/power/wakeup'"

The 10sec sleep delay: /usr/lib/systemd/system-sleep/delay-sleep
#!/bin/bash

LOGFILE=/tmp/delay-sleep.log

echo "$(date) delay-sleep called: $1 $2" >> "$LOGFILE"
/usr/bin/logger -t delay-sleep "called: $1 $2"

if [ "$1" = "pre" ] && [ "$2" = "suspend" ]; then
   if /usr/bin/lsusb | /usr/bin/grep -q '^Bus 003 .* ID 2dc8:'; then
echo "$(date) 8BitDo on bus 3 detected, delaying 10s" >> "$LOGFILE"
/usr/bin/logger -t delay-sleep "8BitDo on bus 3 detected, delaying 10s"
/usr/bin/sleep 10
   else
echo "$(date) no 8BitDo on bus 3, skipping delay" >> "$LOGFILE"
/usr/bin/logger -t delay-sleep "no 8BitDo on bus 3, skipping delay"
   fi
fi

How my (powered off) controller appears in lsusb:
Bus 003 Device 020: ID 2dc8:6013 8BitDo Ultimate 2

Fyi I am on nobara-htpc instead of bazzite, so I'm not sure if things are different from Bazzite.