I would be surprised if there were any SATA drives that also had a play button. The number of people plugging headphones into their CD-ROM drive and playing it without using the rest of the computer had to be incredibly small by the year 2000, let alone 5-6 years later when SATA drives became more common. Also, IDE at least allowed the possibility of using the straight analog audio out of the drive (which you could use the play button for), but I don't believe analog audio output was was a thing on SATA drives at all. If someone knows of a SATA drive with analog audio out though, please post it. I am curious. 😁
(EDIT: Looks like someone successfully modded an analog output to a SATA drive that still had a place for one on the PCB. So, I guess it is maaaybe possible that some SATA drive that uses a similar older style PCB might have also used an older housing that had a play button too.)
Likewise, PCs with black\dark drives weren't common at all until around ~2001 with some OEM models like the Dell Dimension 4200 and others getting the ball rolling.
So, you're looking for a drive that uses kind of an outdated design\housing that still has the play button and headphone jack but was made at a time when it was likely to be used in a black PC... and before they were SATA. Maybe looking at some old PC catalogs from 2001-2004 will give you some brands and models to look for?
EDIT: Aha! I searched for Black 16x DVD IDE drives and found this Dell 0D7191 that has two buttons and a headphone jack on the front:
https://ithardwarehub.com/part-no-0d7191-dell … vd-drive-black/
They seem fairly uncommon, but hey, it's something to look for! Also, it isn't a burner... it is just a CD\DVD reader.
... also, what happens when you have a DVD in the drive and press play in Windows? Does it actually make Windows open up the DVD player? Never thought about this before. 😋