Are you sure S3 sleep is enabled in the bios? On most machines it’s one or the other, not both at the same time. On some Intel machines you can still enable S3 standby, but I know AMD killed it a lot sooner than Intel did.
Windows has powercfg /availablesleepstates to show what states are supported. I’m sure there’s something like that for linux but I’m not 100% sure. You could try dmesg | grep -i “acpi: (supports”