The macOS is Mojave. I have now checked the battery schedule and that is not the cause. Also there are no "StartCalendarInterval" commands in any of the .plist files.
The log.txt has 390 searches for "wake", these are the first few:
2023-07-25 21:15:00.005376+0100 0x74 Default 0x0 0 0 kernel: PMRD: System Wake
2023-07-25 21:15:00.007331+0100 0x47c4f Default 0x0 128 5 loginwindow: [com.apple.loginwindow.logging:Standard] SleepWakeCallback_block_invoke | enter. messageType=0xe0000320, gPerformSleepWakeActions=1, userSwitchedOut=0, screenIsLocked=1
2023-07-25 21:15:00.007332+0100 0x47c4f Default 0x0 128 5 loginwindow: [com.apple.loginwindow.logging:Standard] SleepWakeCallback_block_invoke | kIOMessageSystemWillPowerOn, isMainThread:0
2023-07-25 21:15:00.007334+0100 0x47c4f Default 0x0 128 5 loginwindow: [com.apple.loginwindow.logging:Standard] SleepWakeCallback_block_invoke | exiting
Unfortunately I do not know what this information means, even though I have searched the internet.
The iMac wakes on my side but tonight I will leave it on my wife's side and see if the same thing happens. Again, thank you for all your suggestions.