I’m not clear on what you’re trying to say. The “deep” option in /sys/power/mem_sleep is S3. The “s2idle” option is S0.
For me at least, when using “deep” the delay is around 12 seconds. For “s2idle” it’s already awake by the time I get the lid raised.
# cat /sys/power/mem_sleep
[s2idle] deep
This would indicate that you’re using s2idle.
# cat /sys/power/mem_sleep
s2idle [deep]
This would indicate that you’re using deep.