Blu-ray drive desktop icon missing

I have a guess what may be going on. And it's that Apple has changed where it looks on a Blu-ray disk for the icon. See this topic:

Any way to see new Blu-Ray icons? - Apple Community

Per my test, yes, newer versions of macOS will indeed display a Blu-ray disk icon if it's located on the disk where macOS looks for it. Older disks (and virtually any commercial disk it seems) don't write the icon where macOS looks, so you get nothing.

However, it's still Apple's error. You can't blame billions of Blu-ray disks that worked as expected before Catalina. Apple should be looking in both the newer and traditional location for the disk icon, but aren't.

For static things that do not change over time, then your BD-R solution may be ok, but Time Machine gives you more flexibility for retrieving things that change over time, or that you want to retrieve from a specific timeframe in the past, or repave an entire operating system and your data on the drive.

Since the operating system does not natively support Blu-ray, Apple does not provide a Blu-ray icon for a mounted disc when it is mounted. I've noticed that with my new Pioneer BDR-X13U-S with Blu-ray or UHD 4K discs mounted. Nor does it provide a right-click Eject button, as that functionality remains under the Finder Windows mounted devices in Locations.

Blu-ray disks showed an icon all the way through Mojave. Then, for whatever reason, macOS stopped showing them beginning with Catalina.

Why? Who knows. Blu-ray was just as "unsupported" 12 years ago on the Mac as it is now, but the icon issue is fairly recent.

Some notes I've read online have people saying, "Well, maybe your disk doesn't have an icon." This is clearly wrong since any Blu-ray disk I put in the drive under Mojave displays on the desktop. So, the icon is there, but later versions of macOS aren't reading it.