You can't write to any UMDs, but you could technically connect a regular PSP to your PC via USB and VHS menu allows you to let the USB connection expose the UMD to your PC like a regular external drive.
However, again, you can't write to any UMDs, you can only read from them. And afaik there are currently no media players that can handle the raw UMD data you can access this way.
The closest thing you could reasonably get to an actual DVD drive with similar aesthetic would be MiniDisc. Specifically either any of the HiMD recorders that can handle up to 1GB HiMD media and function basically like an external USB drive, or one of the NetMD recorders which do the same but can only handle regular MD with a max capacity of 330MB per disc. Those discs are basically rewritable up to a million times, but the recorder and HiMD media are pretty damn expensive and read and write speeds aare generally limited to USB 1.0, so 12MB/s in the best case scenarios.