Realized I never made a recommendation. Duh. I’d highly suggest going with a separate amp and DAC as it gives you better quality and more flexibility going forward and they don’t take up much space — at least not the ones I’m recommending. If you’re open to tubes I’d highly recommend the Quicksilver Headphone Amp, which I view as quite a bargain at around $1200…
http://quicksilveraudio.com/products/headphone-amplifier/
If you’re looking to spend less, the Singxer discrete, fully-balanced Class A amp produces that smooth Class A sound at only $599 — I own it BTW…
For a DAC, the Musician Pegasus is great (I also own it) and is also a bargain at $1044 IMHO, but if you can spend around $600 more the Gustard R26 will likely give a good performance boost — both are R2R DACs BTW…
https://www.amazon.com/Musician-Pegasus-Decoder-DSD1024-Amplifier/dp/B0891SPSWJ/ref=sr_1_1?crid=1QEHF5RBVVG8N&keywords=Musician+Pegasus&qid=1677792285&s=electronics&sprefix=musician+pegasus%2Celectronics%2C138&sr=1-1
Also, if you get a DAC with an i2S connection (as the ones I recommended both do) I also highly recommend getting a DDC to be able to take advantage of this connection as it made a huge difference over using an SPDIF connection and it also re-clocks the data. The Musician Pisces or Denafrips Iris (which I own) would be great choices. Sorry for being so late, but hope this helps and best of luck.