Time Machine could not complete backup

some Bus-powered drives do not respond well if the Mac sleeps. The USB ports transition to USB standby power mode, and some drives can't cope and just disconnect.

When the drive comes back to life, you Mac may report the drive was ejected improperly.

In some cases, the drive needs a disk Utility 'repair disk' to be made well again.

if you have a steady power source for your external drive, that would be better. Otherwise, Make sure your Mac does not try to sleep while a backup is in progress.

in rare cases, the notification is stale, and the drive was re-acquired, the backup has made progress, and possibly even completed. The notification, once issued, can not be retracted.

So check for the current Time machine status before you get too excited.

This may sound tangential, but read all the way to the end.

Time Machine works very nicely with multiple drives attached. Every-other backup goes to every-other drive, and each drive is independent of the other. Either drive can be removed whenever you choose.

if you start now, it will make a full backup on the new drive, and start to add incremental backups every two hours. By next week you MAY be willing to erase the old drive. Then you are never 'working without a net'.