The DT770 is fine – not basshead, the COP is the same size and configuration as the 770, and both of those, large though they are, are “tighter” built so they feel less clunky than the M50. But the biggest problem for you is that the smaller headphones under $200 almost all have a steeply rolled-off treble, which is trouble for the more refined type of music. One possible exception is the Harman Soho.
I’ve never enjoyed the audio quality of Bluetooth headphones, but that’s just me. The sound is better than it ever has been, and it’ll get you 90% of the way there—but not everybody is willing to make that tradeoff. Since USB-C headphones have largely ceded their market advantages over Bluetooth, we have to examine the consumer audio technology’s performance in a world where the headphone jack is disappearing.
I think it’s fair to compare the Grados and HD598, but the M50 is very different and seems not to fit in that comparison. The DT770 is a better comparison to the M50, although the 770 is a better more expensive item. A long time ago I had a Grado 325 and a Sennheiser HD565 – very similar, very enjoyable. Today for that type of sound I might choose the Soundmagic HP100.
In-ear headphones are like earbuds but are an upgrade to them. These headphones fit into the wearer's ear canal and stay in place with the use of foam or rubber tips. These tips are available in custom sizes so they can fit each individual wearer. When a proper fit's achieved, in-ear headphones reduce outside noise and deliver sound quality at about the same level as over-ear and on-ear headphones.