Your drive is NOT BROKEN! I've had the same problem with a 2TB Seagate external USB3 drive on my ASUS Zenbook running Windows 11. The drive works fine on my HP laptop running windows 10. But on the Zenbook, it temporarily recognizes the drive, gives it a drive letter in Explorer and, promptly disconnects. Repeatedly!
It's almost like the anti-virus software in Windows 11 is disabling the USB driver after the drive is connected, because it falsely detects a virus. This is the case even after I format the drive on my HP laptop running Windows 10.
Interestingly, I have USB external hard drives manufactured by Western Digital and by Hitachi which works just fine on that Zenbook running Windows 11. So, the problem is definitely between Seagate and Microsoft. They need to update the USB drivers for Windows 11 to fix this problem!