Since you have mentioned that your new iMac shipped in 2019 and your old iMac read the memory card well, I guess you need to check the file system of your Sony SDCX card in Disk Utility to see if it is still supported by your new iMac.
Here I am gonna show you how to check the file system of your SDCX card in Disk Utility:
Step 2: Click View and select Show All Devices.
Step 3: Your SDXC card should appear in the left column with its volume. Select the volume and look for the volume format near the top of the window.
If it shows Mac OS Standard of HFS instead of Mac OS Extended or HFS+, then that's the problem. macOS Catalina dropped support for the older volume format that was replaced in 1998.
If you want to make your SDXC card readable by your new iMac, you need to format it to Mac OS Extended or HFS+. Be careful to perform a formatting task because it wipes everything on your memory card.
For more details about formatting the SD card, please read the related article: How to Format (External) Hard Drive for Mac and PC? A Stepwise Guide