dvd r/rw external drive is not recognized by macbook pro

I think you may be out of luck.

You can check if the drive is recognized in the System Report. You can find that from the menu bar under

apple/About This Mac, then More Info, then scroll to the bottom and click System Report

Or, for older Macs,

apple/About This Mac, then click System Report.

Scroll down under Hardware to USB or Thunderbolt/USB. You may need to click through the "device tree" on both of them to find your disk drive - or, it may not register at all.

I connected an LG CD/DVD drive to a 2021 MBP 14" running Sonoma, and it didn't show up in the System Report, even with a disk in it (through a dock that provides power).

The drive appeared in System Report, and the disk appeared on the desktop, on a 2013 MBP 13", running Big Sur.

You might be able to download a driver from the manufacturer's website, but check the documentation. LG had driver updates, but only for Windows.

On a Mac, the drive doesn't actually show up on your desktop.

When you insert a CD or DVD disc (blank or recorded) into the drive, the disc will show up on your desktop.

In order for us to respond you first need to provide us with more specifics. What is or is not happening when you do something. Also, you should know that just connecting the drive does not "activate" it. It will show up on your desktop and can be opened only when a disk has been inserted that has been properly formatted and has a file on it that can be recognized,