How to VNC connect to a sleeping iMac?

I use RealVNC to connect to an intel-based iMac, but it cannot wake it up if it is asleep after long inactivity. Yes, I don't change the setting to prevent from sleeping but only leave 'Wake for network access' on. **However, the same works perfectly to connect a sleeping Mac Studio**. This obviously has the merit of letting the machine rest and saving energy. Both 'server' machines use WiFi and the other machine used to control them is *not* necessarily within the same local network. The 'server' machines **do not have a public IP addresses**. I tried to compare the settings like in 'Energy Saver' between the two host machines, but still have no clue. When testing this, I noticed that I still can connect to the iMac right after (like 10 seconds) I manually put it to sleep. If I wait a few minutes, it does not work.