You have a 70 Ω resistor (R8) in series with the coil and that will stop the relay operating. Given that the relay coil has about 70 Ω internal resistance, the external resistor will effectively prevent anything other than about 2.5 volts being applied to the relay coil. Hence, it doesn't work.

Picture from here.

The coil power is about 0.4 watts and, from 5 volts that means it needs to take about 80 mA hence, it's internal resistance will be about 5/0.08 Ω = 63 Ω.

The BS170 MOSFET will drop a little bit of voltage but, to me, the big show-stopper is R8.

You have a 70 Ω resistor (R8) in series with the coil and that will stop the relay operating. Given that the relay coil has about 70 Ω internal resistance, the external resistor will effectively prevent anything other than about 2.5 volts being applied to the relay coil. Hence, it doesn't work.

Picture from here.

The coil power is about 0.4 watts and, from 5 volts that means it needs to take about 80 mA hence, it's internal resistance will be about 5/0.08 Ω = 63 Ω.

The BS170 MOSFET will drop a little bit of voltage but, to me, the big show-stopper is R8.

OK, if the gate-source voltage is only 3.3 volts then the BS170 could also be a problem. The graph above from the data sheet shows that with a 4 volts gate-source drive voltage, it should be OK but, at 3.3 volts, it may fail to operate sufficiently.