Just add to what my colleague @den.thed has already suggested
If the MacBook Pro battery ran out while Time Machine was writing to the WD Elements drive, the problem may be as simple as the USB connection needing to be reset, or it could indicate filesystem corruption or a hardware issue.
The fact that the drive is not visible in either Finder or Disk Utility is the key symptom.
First, determine whether macOS detects the drive at all.
Open Terminal and run diskutil list
Then run system_profiler SPUSBDataType
If the drive or "Western Digital" appears in the output, macOS is detecting the hardware and the problem is likely with the filesystem. If it does not appear, the Mac is not communicating with the drive.
Next, disconnect the drive, completely shut down the Mac, wait about 30 seconds, reconnect the drive, and power the Mac back on.
Also try a different USB cable, another USB port, or a different USB-C adapter if one is being used.
Open Disk Utility, choose View > Show All Devices, and see whether the physical drive appears.
If it is listed but not mounted, try mounting it. If mounting fails, run First Aid. Apple describes this procedure here: Repair a storage device with Disk Utility.
If the drive appears in the output of diskutil list, you can also try: diskutil mountDisk /dev/diskX
Replace diskX with the correct disk identifier reported by diskutil list. If mounting fails, note the exact error message.
If the drive does not appear in Finder, Disk Utility, diskutil list, or system_profiler, the problem is likely a faulty USB cable, an issue with the drive's USB interface, insufficient power, or a hardware failure.
Testing the drive on another Mac ( as @den.thed has suggested ) is the quickest way to determine whether the issue is with the drive or the Mac.
If the drive is detected but will not mount, you can verify the disk from Terminal with diskutil verifyDisk /dev/diskX
Because the interruption occurred during a Time Machine backup, it is possible that the APFS filesystem or the backup was left in an inconsistent state. However, filesystem corruption alone would not normally prevent the physical drive from appearing in Disk Utility or diskutil list.
Apple's documentation on Time Machine is available here: Time Machine User Guide for Mac.
To narrow down the cause, it would be helpful to know the output of diskutil list, the output of system_profiler SPUSBDataType, and whether the WD Elements drive is a portable USB-powered model or a desktop model with its own power supply