I am unable to copy file from my MacBook Air OS 12.6.3 to Extreme SSD (format APFS). That said, the Time Machine seems to be backing up to it just fine.
Have you opened a Support Case? If not opened, for more information, please contact the SD Technical Support team for best assistance and troubleshooting:
On your Mac, select the item, then choose File > Get Info or press Command-I.
Click the arrow next to Sharing & Permissions to expand the section.
Click the pop-up menu next to your username to see the permissions settings.
If you’re not logged in as an administrator, you may need to click the lock to unlock it, then enter an administrator name and password (or use Touch ID or your Apple Watch).
Change the permissions to either Read & Write or “Read only”.
If you need to, also change the permissions for the location where you want to put the item.
Remove unnecessary files to save space.