Headphone audio is like room audio. Every aspect controls the output you hear. The electronics must support the output device. Headphones need amplification that supplies the clean, natural signal and raw power, more importantly the current the headphones require. Yours clearly require lots more power.
Given your investment level… assuming you want to stay in that range you want headphones that are easy to drive, that require very little current. I’m sure lots of folks here can recommend some. Or you can get a much higher quality headphone amp.
You can see my headphone system under my UserID if you want to see what a great sounding system can look like. Yes, that is all for just powering headphones.