>I started to worry that I was not careful with them enough and they simply don’t have the same quality anymore, but I don’t know how to check if that is the case.

Headphones don't wear out. Not to any degree that matters. The only thing that does wear are the pads, and that's just through use. You should replace them periodically.

>However, how it happens with all addictions, I start to feel like it is not enough and my headphones sounds not as great as I thought. I started to notice sharp sounds in lyrics, missing details, kinda like “flat” sound in places and so on.

Step #1 would be to stop overanalyzing. Your listening experience can be influenced to a huge degree by your own perception. If you want to think there's something "wrong", you'll most likely find something, even if that something is entirely in your head. So try to chill out a bit on that front.

Beyond that, the biggest thing you're missing as a beginner is experience. You need some reference to know what stuff sounds like and what you personally enjoy. The easiest way to do that is to check out a hifi store near you if possible.