I use and have very good results with Safer Brand Horticultural Spray. My lemongrass, mint, and chard got infested with aphids and this stuff got rid of them immediately. It's non toxic, which is pretty awesome. I've also used it on other plants to get rid of flea beetles. Some plants can be sensitive to it but so far, tomato plants seem to be the only plants that didn't respond well, every other plant couldn't care less. The tomatoes didn't die, they just got some yellow leaves and then eventually rebounded after a week or two.
My lemongrass got a nasty aphid infestation recently (which was surprising since lemongrass is often an ingredient in sprays meant to deter aphids). I cut the lemongrass down because it was too difficult to spray otherwise and used Safer Brand Insecticidal Soap in case there were any aphids still hiding around the base of the plant. It worked really well - the lemongrass grew back with no sign of aphids. I've also used this spray successfully on other plants like chard that got infested with aphids, and mint and cucumber that had flea beetles and it seemed to work (though they do come back periodically and I have to respray). Some plants are sensitive to this spray, like tomato plants for example, They didn't react well to it, but they didn't get killed or anything and they rebounded after a few days.
They look like scale insects, they can be controlled by spraying them with horticultural oil (it suffocates them) horticultural oil:https://www.amazon.com/Safer-5192-6-Brand-Horticultural-Concentrate/dp/B07GFWBSJ4/ref=sr_1_13?dchild=1&keywords=horticultural+oil&qid=1607563089&sr=8-13
If they're mite eggs, mites are very destructive. All things being equal the horticultural oil wont do any harm. https://www.amazon.com/Safer-5192-6-Brand-Horticultural-Concentrate/dp/B07GFWBSJ4/ref=sr_1_11?dchild=1&keywords=horticultural+oil&qid=1607487672&sr=8-11
Be careful with hydrogen peroxide; I used it on some of my plants after reading some articles about how well it worked and it ended up killing several plants. So if you decide to try it, test it out just on one leaf to see if the plant can tolerate it. I had it diluted 1:3 and it was still way too strong. I eventually used the ratios given in this video from by the Rusted Garden and it didn't kill my plants anymore but even diluted that much, some plants still didn't respond well to it. A few did respond really well to it; oregano and chard in particular seemed to grow much better after a few diluted peroxide sprays.
I use a liquid castile soap (like the one you showed, but not peppermint - it's unscented) for aphids. I squirt a tiny amount into a 16 oz spray bottle, add some neem, and fill it with water. Then I shake the bottle in between sprays. So far, I haven't noticed any problems. I also use an insecticidal soap spray from Safer Brand that works well (though some plants like tomatoes are really sensitive to it, I haven't used it on peppers). Try spraying it on just a few leaves and if the plant is fine by the next morning, it should be no problem.