So, just to ignore your budget, I have the Sony XM4 headphones (over ear), and… they are okay. In the heat, they get very sweaty, and there are annoying sounds you can’t turn off (on/off beep, and a voice which tells you when it has connected). The noise cancellation is good for constant noises but not sudden ones. Overall, I wouldn’t recommend/buy them again, as they are just fine.

I have tried some in ear ones from Xiaomi (not sure which exactly) which I bought for my partner, and they are, in my limited experience, just fine too, especially for the price (<$50). I don’t know about any long-term idiosyncrasies though, so take that with a pinch of salt. These ones look a bit better: Redmi Buds 5 Pro. www.amazon.co.uk/…/B0CQKHK626/

The noise cancellation is good for constant noises but not sudden ones.

This is kinda the nature of active noise cancellation, unfortunately. Blocking out sudden noise is just technically very challenging. Works great for airplane noise, not so much for crying babies.

Sony’s XM line is in my opinion just about the best ANC headphones money can buy, in terms of noise cancelling and sound quality combo. I can understand your point about them getting sweaty. Part one of blocking noise is good sound insulation, which tends to hold in heat as well. I live in a colder climate so that works out well for me. You could get in-ear ones, although obviously they don’t block out noise as well.