iMac spontaneously wakes from sleep

Perhaps Bitdefender is running a scan.

Most of the regular forum contributors recommend uninstall all anti-virus software, cleaning & optimizer apps, and third party security software because none of it is needed on a Mac. These types of apps usually cause more problems than they solve, plus they interfere with the normal operation of macOS. Uninstall all such apps by following their developer's instructions. I would definitely start here before doing any other troubleshooting.

It is also possible other apps & services are trying to do background maintenance. They won't know WiFi is off until they start their processing & discover no network.

I understand, but why did it appear suddenly? I have used BitDefender for a long time.

It is annoying to have to shut down the Mac all the time since it takes a pretty long time to start.

If I remember correctly Windows ha a "hibernate" option instead of shutting down that was quicker.

Something similar in MacOS?

I have uninstalled BitDefender but the problem persists. In sleep mode and with WiFi disabled and logged out the computer still awakens after about half an hour and then stays under screen saver.

I hav absolutely NO idea of what is going on.

Sleep is one of those features that has always seemed to have a mind of its own. All my Macs frequently wake up from sleep all on their own. No explanation. There have been many threads about this, you are not alone.