Samsung Portable SSD app not recognizing T7 Shield SSD on MacBook M2 Pro

If the drive shows on the desktop, the Mac already sees it. The Samsung app is separate and needs its own software allowed.

On the M2 Pro, do the same startup security change you did on the M1. Shut down, hold the power button, open Startup Security Utility, set Reduced Security, and allow user management of kernel extensions. Then in System Settings, Privacy and Security, allow the Samsung extension and restart. Normal copying works without that app.

You would be better off uninstalling and not using that Samsung app. The fact that you have to reduce security to use it should be enough to tell you this is a bad idea. Drive manufacturers often provide these apps but they often turn out to be incompatible when the macOS is updated ad this can actually cause a loss of access to the data on the drives.

You can and should manage the drives with Apple's Disk Utility and nothing more.

Not knowing what dependencies have been introduced with that Samsung app, what I would do is copy all the external drive's contents to a different drive. Then I would erase/format the T7 with Apple's Disk Utility and completely uninstall (with an uninstaller) the Samsung app and remove it from your Mac. Then I would restore security to its proper settings. And restore the saved files back to the newly formatted T7.