What is the easiest way to make a discrete sensor for the presence of a small alternating current?

Question

Electronics

Given:
There is a chandelier with 6 horns. It has 5 ordinary bulbs and one "smart" bulb screwed into it, for example, Mi Smart LED Bulb 8W (WiFi).
Power is supplied to the chandelier constantly 220V (the switch is always on).
The power of the smart bulb is 8W, when the bulb is turned on at full brightness, that's exactly the power I was able to measure with a smart Yandex socket. When the light is turned off or not turned on at full power, the socket says that the load is 0W, apparently there is not enough accuracy.

Task:
It is necessary that when the smart bulb is turned on, the blunt ones turn on, and when turned off, they turn off.

How did you plan to solve it:
We connect a small power supply for 220V-> 5V in parallel with a smart light bulb. We hang the current presence sensor on the circuit of a smart light bulb, set the response threshold. When the specified current threshold is exceeded (when the light turns on), we send a signal to a solid-state relay (Omron controlled from 5 volts), and it supplies linear voltage to the rest of the chandelier bulbs.

Question:
How to make a current sensor so that it can distinguish the current of the on light bulb from the current of the off one (after all, Wi-Fi works constantly in it)? The signal from the sensor must be discrete in order to be able to control the relay.

I see the following solutions:
1. Wind the coil with a large number of turns, and instead of the core, pass one of the power wires of the smart light bulb. Take a signal from it, rectify it with a Schottky diode and apply it to the gate of a field-effect transistor or a Darlington pair in order to control a relay through it.
It is not clear whether the induced current will be enough, the more there will be a voltage drop across the diode or double on the diode bridge. How to properly smooth out pulses of 50 (or 100 hertz, if the diode bridge) so as not to pull the relay and the load with such a frequency? How to choose a transistor? How to adjust the trigger threshold? How to properly rebuild from interference, or maybe they will not exist at all?

2. Wind a transformer with a low-resistance primary winding and a large number of turns in the secondary. Otherwise, as in the first option, only turn on the primary winding in series with a smart light bulb.
How to calculate a transformer? Plus questions from 1 point.

3. To somehow adapt the hall sensor to determine the presence of current, maybe wind around it a few turns of the power wire of a smart light bulb or somehow attach a ferrite ring ...
It’s not at all clear here. What hall sensor? How to attach it correctly? How to take readings and is there enough sensitivity?

4. Use the shunt in series with a smart light bulb and, having received a divider, remove voltage from the shunt, straighten it and otherwise, as in the first paragraph.
It is not clear whether such a divider will work normally if there is a pulsed power supply in the light bulb, how to calculate the shunt, how to properly remove the voltage and set the response threshold (see point 1)

5. Attach a photo-resistor shaded from other sides to the smart bulb and control load according to his testimony.
Somehow inelegant. Plus, it is possible that the photo-element will be illuminated by other bulbs or daylight, which will provoke the inclusion of a controlled load. It is also not clear which photocell, how to adjust the threshold ...

6. Open a smart light bulb, find where to solder and power the solid state relay directly from it. Maybe there will be enough space in it to make a plug ...
Absolutely that porn. Not safe, not universal, hard to replace a smart light bulb just in case...

If the described device could be made sufficiently compact, simple, inexpensive and reliable, then such a solution, it seems to me, would be very popular with those smart home builders who are forced to put up with old wiring and Wi-Fi to control the light.
Smart bulbs are almost half the price of smart sockets and any relays controlled via Wi-Fi, but they usually give little light per room, and a lot of smart bulbs in one chandelier is both expensive, and the load on the router is unnecessary, and pointless, and merciless.

Answer 1

from the article Simple dependent load switching device

Answer 2

Attention: I did not make any particularly serious calculations, it is advisable to carefully check everything on the layout.
ACS712 is a Hall current sensor that outputs the value of the flowing current as a voltage. Characteristic - 185mV / A. I think the real waveform of the current through the switching power supply will consist of needles that the sensor will see.
ACS725 features almost double the sensitivity (264mV/A)
LM358 is an operational amplifier. We take the signal from the sensor, multiply it by 10 times (on one half of the LM358), then on the second half we make a threshold element - a meander will come out of it if there is a load.
We smooth the meander with a capacitor and let it go to the transistor, which is already pulling the relay.
Something like this. The remaining spare parts - resistors and capacitors - can be taken from datasheets for microcircuits. A transistor to control the relay - yes, even the Soviet KT815-817-819 or the bourgeois TIP42C (to be sure). Relay - what you find for 5 volts. You can even use an opto-relay in the collective farm if you don’t want to listen to the clicking.
The advantage of the circuit is that it will not be galvanically connected to the mains voltage - in the ACS712 the connection is magnetic. Well, you don't need to wind anything.

Answer 3

Current transformer -> rectifier -> filter -> comparator with adjustable threshold and hysteresis -> relay. Don't forget to add a power supply for all that good over-current/voltage protection, and it turns out that it's not easy to make such a device "small, simple, inexpensive and reliable". As a sample, take a ready-made electronic current relay and look at its circuitry.