I'm trying your circuit in an animated simulator found at:
www.falstad.com/circuit
Here is a screenshot:
The shot is in mid-cycle.
I find that there is current flowing only through the bulb. Very little current flows through the other components.
I adjusted specs for the bulb to draw a few mA.
When I disconnect the 9V battery multisim does not want to simulate. (simulation error)
This simulator permits me to disconnect the battery.
As for when I disconnect grid power...
The battery powers the bulb slightly, however it is because current goes through the 2200 ohm resistor and gate of the scr. Current does not go through the scr proper.
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Your circuit is a good try.
Configuring an scr circuit is not the easiest task. We must determine what polarity is correct for the gate drive? Where should ground be? Where should the load be?
I find that Falstad's animated simulator makes it easy to examine operation of circuits. To see for yourself, you might like to try your circuit in it. It's free.
To use an scr, it would help if you start with the simplest circuit and get the scr to power the lamp. Its gate needs to be referenced to the correct polarity. The load needs to be closest to the correct lead. Etc.
Then start adding the components that will provide backup power.
All this is to say, it's not an issue of getting the calculations right, at this point.