I am using Macs with Mac OS X El Capitan, Sierra, High Sierra, Mojave and Catalina.
I also have Data CD's and DVD's dating back almost twenty years, these disks were written long
before these OS's were released. I can see these CD's and DVD's across all of the OS's mentioned above.
The disks all appear on the Desktop and in the Sidebar under Locations, and any items on the disks can
easily be dragged and dropped onto the Desktop or any nominated folder. These disks contain like yours
images, documents and movies. The majority of these disks would have been created using Toast Titanium
and using a disk burning protocol that would make disks readable on both Macs and PC's.
Can you remember how your older CD/ DVD disks were made.
Which OS was your Mac running when you created these CD/ DVD's, if it
was High Sierra and these CD/ DVD's were not 'finished' (the lead out track was not written)
then that might be an answer to why they cannot be read on another Mac or OS,
but still be able to be read on High Sierra.
Any further information on how these disks were created may prove useful.
If there is still no further progress then you can transfer the data on the CD/ DVD's
to an external hard drive, or USB sticks on your High Sierra Mac and transfer the
data to your Mojave or Catalina Mac that way.