555 soft latch triggers when voltage applied and turned off
You have TRIG and THRES set to 1/2 Vcc, so the 555 could power up in either state. To ensure that it is reset on power up you should pull RST low until the supply voltage has stabilized.

Adding a startup delay with 2,2k (or 10k) + 10uF connected to pin 4
and GND - doesn't help on its own

Reset is only active when RST is below ~0.7 V (minimum 0.3 V), so with 10k and 10 uF the reset time will be much shorter than you might expect from the RC time constant. Try a much larger resistance (eg. 100k) to increase the reset time. Also put a diode across the resistor to discharge the capacitor faster on power down.