Hello @Mbrillow 
Smart bulbs always use electricity, after being turn off in the APP, it works in stand by mode at very lower wattage thus bulb can be activated again from APP.

If the relay is off, bulb has no power and could not be communicated with Kasa app anymore.This is how they work, you may replace bulb with an ordinary bulb and use smart bulb for another use.

If Wi-Fi goes down, your phone need to connect to local/home Wi-Fi to control bulb, as remote control requires bulb connecting to cloud service. 

@Mbrillow 

sorry for the delay reply.   Bulb should behave like @ludde28 said: 

Set brightness at 90% for Tapo Bulb

Press switch to turn OFF switch and press switch to turn ON

Bulb should turn on with brightness at 90% 

If you can not turn on bulb when press the switch manually, please  try a different light fixture, and do Not use smart bulb with a dimmer/ switch.

If the same issue, may I know is it a new bulb, can you share the Mac & SN number of the bulb by private message, thank you