AKG Pro Audio K702 Over-Ear Open-Back Flat-Wire Reference Studio Headphones

For classical music and jazz, these are, by far, the best in this price range. Maybe a bit boring for Rock and EDM but I have many other headphones for those genres. If you need a set of headphones for classical, these are highly recommended.

Ignore people quoting the Ω impedance… that is only a third of the equation, and the part to pay the most attention to is the sensitivity, which is 105 dB SPL (concert loud) /V @ 1 kHz (with a volt of output power, a test tone played at the "this is only a test of the emergency broadcast system" tv alarm pitch, it will sound as loud as an average live concert and louder than you should listen). Some headphones have less impedance than the K702, but be much harder to drive because their sensitivity is low.

So, at least the midrange is very easy to drive loud enough, including with the amps integrated inside of typical sound cards, smartphone dongles, and so on. Should work fine from your soundcard. I will say from experience, however, that the QUALITY of the amp will still be revealed by the AKGs, so while both your soundcard, a Sony Walkman ZX500, or a $600 discrete desktop amplifier all can play at equivalent loudness (and a PS5 controller will get "loud enough"), the $600 amp will still help the audio sound more crisp and have a more solid impact of bass attack and cymbal hits.

Beyerdynamic headphones DO use more metal in their designs; the metal materials DON'T inherently make their build "quality" better in the sense of durability, comfort, or acoustic quality compared to the resins of headphones like AKG or Sennheiser… just heavier, with a bit more luster to look at from the metal. All three of these brands make excellent headphones, your audiogram and personal taste will dictate your individual favorite.
Beyer = bright
Sennheiser = warm and bold (HD 800 being an exception)
AKG = somewhere between the two with emphasis on soundstage.
Beats = bass and treble emphasized over mids/vocals, more than just "warm"
Bose = chocolatey but muddy warm sound.