Check if the Paragon NTFS for Mac tool is correctly installed. Chances are that you didn't finish all the needed steps to install the driver and thus cannot write to the NTFS drive on your new M1 MacBook Pro.
The Paragon NTFS for Mac software needs to be properly installed for it to work, which often includes: run the installer > allow the app to open in Security & Privacy > enable system extensions in Recovery Mode > allow the app to launch in Security & Privacy again > restart your Mac > grant gull disk access.
If you haven't completed the installation, finish it first to see if you can write to the NTFS Seagate Backup Plus drive. If it doesn't work, you can use iBoysoft NTFS for Mac instead. It will also require you to enable system extension, which is necessary to install the NTFS driver, but it's less complicated than Paragon NTFS for Mac.
With it, you can read and write to NTFS drives on Intel and M1 & M2 Macs running macOS 13 Ventura ~ macOS 10.13 High Sierra natively. It will automounts your NTFS drive, saving you the time to relaunch the software after a reboot or reconnecting the drive.
You can click the button below to start the free trial.