Question about Ledvance Smart+ Plug

yes works

It works for me.

If there are internet outages, for example, the timer is always there...

Good question, my version doesn't work because the settings are controlled by software, i.e. the plug is stupid, it gets the commands from outside.
If you switch off the wifi, the plug no longer receives any commands.
So without wifi, the plug cannot receive the signal to switch on.

What you need is an analogue or digital plug, but not a smart plug.