Time Machine can't switch to new external Seagate hard drive

it does not require you to SWITCH. You can ADD an additional Time machine drive at any time, and backups will alternate -- every other backup to every-other drive.

Time machine will ask to Initialize a drive it is not in an acceptable MacOS format already. If time machine refuses the drive completely, ERASE the PHYSICAL DEVICE using its immutable manufacturer-given device-name to some random format like ExFAT, and then try again:

Erase and reformat a storage device in Disk Utility on Mac - Apple Support

Hi,

Perhaps the article Change Time Machine preferences on Mac – Apple Support (UK) will be of some help.

From that, what the solution looks to be for you is to open Time Machine with the new disk connected, click add a new backup disk to add the new disk as a backup destination and then click remove backup disk to remove the old drive.

Hope this helps :)

What Format is the new drive?