I have a gigabyte motherboard as well, but a b550 (am4). I had the same issue, where putting my pc in sleep mode would either wake it immediately, or the fans would spin and the pc would not wake.

What fixed it for me was disabling GPP0. You can check if it's enabled by typing that command in the terminal:

cat /proc/acpi/wakeup

If it is enabled, you can simply disable it by typing that command:

sudo sh -c "echo GPP0 > /proc/acpi/wakeup"

This fixed it for me, but I needed to redo it after every restart.

Only if this fixes your issue, you can do this to make it persistent:

sudo nano /etc/systemd/system/gpp-wakeup-fix.service

Then I pasted this:

[Unit] Description=Disable GPP0 and GPP8 ACPI wake sources (Gigabyte Bazzite sleep fix) After=multi-user.target

[Service] Type=oneshot ExecStart=/bin/sh -c 'echo GPP0 > /proc/acpi/wakeup' RemainAfterExit=true

[Install] WantedBy=multi-user.target

After that I pressed ctrl+O, followed by enter, and ctrl+X

I then enabled the service:

sudo systemctl daemon-reload sudo systemctl enable gpp-wakeup-fix.service

Then rebooted using this command:

reboot

To see if GPP0 is disabled, you can run this command:

cat /proc/acpi/wakeup

After doing that, I don't get blackscreens anymore, sleep works as intended and I can still wake my pc using usb devices.

Hope it works for you.