I will repeat - forget about chipset control in DVD drive.
Internal PATA and SATA drives for computers have all what is needed built in drive itself. FYI: External USB drives internally are PATA or SATA with USB adapter as well. Even those hideous drives where USB to SATA adapter is a part of drive controller circuit and is located on same PCB
For your luck PATA and SATA over USB was standardized 15+ years ago. And are supported by all major operating systems. Windows, Linux, MacOS, ... pick your poison. So same HDD/SSD/CD/DVD/BD/Flash drive which worked in Windows 7, works in Windows 10 as well. USB 3.0 drives over USB 2.0 port will work with USB 2.0 speed, but otherwise they are equal. The only issue you can experience - when external drive without power supply can't initialize because particular USB port can't provide enough current to power connected device. Which again does not apply to devices with power supply in themselves like your adapter about what we are talking about.
USB 2.0 data transfer speed (480 Mbps aka 60 MB/s) is enough for DVD writing and always was. Your usual DVD writer drive with
10x DVD write speed require constant 13.2 MB/s data transfer speed support which USB 2.0 and your USB 2.0 to SATA adapter can easy handle. Avoiding unwanted system load spikes on older/slower systems with 1-2 core CPUs during writing is much more important here. If write buffer exhaustion happen, slow down write speed a little at next time.
There are not much to do with internal 3.5" DVD drive using as external drive via USB adapter. Except avoid splashing coffee over it (and do not allow your cat/children to do it) and do not use very bad +5V/+12V power supplies. If you want to use your "external 3.5 DVD drive" often, maybe put it into some protective casing.
And yes - optical drive as any sophisticated electronic circuit, has capacitors too