I have used dish soap and water as a dip with no adverse effects, I use about ½ ml in a 15 liter bucket of warm water approx 20°C, and I have another 15 liter bucket with clear water again at again at 20°C.
I turn my plant upside down holding in the soil and dip in and out of the soapy water and with the plant still upside down I then shower it down and then dip it in the clear water, and then re-shower it down again with clear water.
I do this every three days for two weeks (actually 5 times), all the time inspecting for live bugs between washes, then when the two weeks are up I stop the wash dips but continue periodic inspections for mites every few days, if I see a new mite I start the bug wash procedure again.
It hasn’t killed my plants yet, but I think it probably would if I didn’t fully hydrate my plants first and if I didn’t wash the soap off immediately.
The soap is just a surfactant and allows the water to drown the mites killing them on contact so it doesn’t need to be left on the plant, and as long as the plant is fully hydrated so that the stomata are closed, the plant can take it.
Only use dish soap that is not antibacterial and doesn’t contain bleach, usually the cheapest ones that just say surfactant on the label. You just need enough of it to be able to make bubbles.