Monterey macOS creates problem in backing up with external Samsung Portable SSD

I have issues in taking backup with Samsung Portable SSD (1 TB) after upgrading my MacBook Pro 15 to Monterey macOS. The SSD is connected to the system using a Type C to Type C cable (without any dock).

When I connect the SSD to my laptop, I get a "Software Installation" popup "Samsung Portable SSD drivers are mandatory in order to use Samsung Portable SSD Software. Do you want to install the drivers?". After clicking on all steps for installing it, I get a message, "This package is incompatible with this version of macOS. The package is trying to install content to the system volume. Contact the software manufacturer for assistance."

I have been backing up in the SSD for 2-3 years (formatted with APFS). I backed up the last time in September 2021, and now I'm trying to back up again in January 2022. Furthermore, I can not afford to format the disk.

Also, trying to enter into the Time machine application hangs my system. I had to restart it.

The Samsung Portable SSD software (automatically opened) does not recognize the SSD and shows no SSD is connected.