I'm not sure if this will be helpful as I don't listen to drama CDs too much (I play otome games more often), but I have before and do sometimes (and I want to start listening to them more). I use Focal Elegia headphones to listen to all audio in general. This model is discontinued, but the company, Focal, sells other headphone models that you can check out (Focal Celestee might be the most similar to Elegia as basically its successor).
I personally enjoy the audio from my headphones and think it's quite high quality, and I'm sure all of the brand's products are just as if not more high in quality as well, but as a more high-end brand, they're definitely very expensive (I was lucky enough to be able to buy my one at a heavy discount and I recommend that people search for those for whatever they purchase) so there are probably more affordable options available that meet others' needs better.
In terms of otome games and CDs, I think my headphones capture all the voices clearly without ever sounding harsh or grating, although the headphones themselves are relatively bulky/heavy, which doesn't bother me personally but might not be something some people want (like for the following reason). If you want to listen to CDs for sleep or while lying down, over-ear headphones might not be the best idea as they can be bulky and get in the way while lying down. There are some that are definitely more lightweight, but I personally still am afraid that they will be crushed when lying down (so maybe earphones would be better for that). I don't listen to anything as I sleep or when lying down, so I prefer over-ear headphones as I prefer the audio quality and they feel more comfortable to me.
Something to take into consideration as well are open-back vs closed-back headphones. Open-back headphones leak sound, so basically everyone around you can hear what you hear, so that might not be what you want if you want privacy, like if you don't want people hearing your otome CDs lol. That probably doesn't matter if you're alone though. My Elegia headphones are closed-back (again, they're discontinued but there are other closed and open-back headphones sold by Focal and of course other brands) which I prefer because I feel like the point of headphones (over speakers) is the privacy. Some people say open-back headphones sound better and more immersive though (wider soundstage, etc. so probably a more spacious, expansive feeling).
My headphones are wired which I strongly prefer, but I am aware that most smartphone models nowadays have no headphone jack so you'd need an adapter to use wired headphones on these types of phones. For this reason, wireless may be preferable for some people and for more freedom of motion? But I personally don't really like having to charge them and in terms of earphones or earbuds, they're much easier to lose if wireless.
I'm not an expert on any of this (and I probably repeated things people already knew - sorry), but I hope this is still a little bit helpful?? Sorry for the length.
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I also use the random earphones I've had since high school. Good luck tho! I hope you get new headphones soon :3 also thank you to everyone for sharing their earphones/ headphones! i'll look into them and get what suits me